# Forecasting Travel Sentiment under the Shock Effects of COVID-19 and Vaccination Using Grey Prediction Models

Authors: Cheng-Wen Lee; Peiyi Kong
Journal: Journal of Mathematics
 (2023)

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## Abstract

The tourism industry has become a major contributor to the economic growth. However, because of the outbreak of the coronavirus disease (COVID-19) pandemic, the year 2020 became an extremely difficult year for the global tourism industry. Since the development of the tourism industry depends largely on changes in travel sentiment, it is important to analyze these changes in light of the pandemic. To determine the development trends of travel sentiment, a hybrid grey prediction model was used to predict travel sentiment globally and in the top 10 destination countries considering the shock effect of COVID-19 and vaccination. The results showed that the grey prediction models integrated with residual modification model contributed to improving the prediction accuracy. In addition, COVID-19 and vaccination were found to have opposite effects on travel sentiment. Based on the predictions, governments should strengthen pandemic prevention and control and administer vaccines to restore travel sentiment and promote tourism recovery.


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## Body

## 1. Introduction

The World Travel and Tourism Council [1] reported that travel and tourism is one of the world’s largest sectors and has gradually become a major source of contributor to GDP. According to Statista [2], the average contribution of travel and tourism to GDP from 2000 to 2019 was 10.14%, reaching 9.6 trillion USD in 2019. However, since the outbreak of COVID-19, the total contribution of travel and tourism to the global GDP declined to approximately 4.8 trillion and 5.8 trillion USD in 2020 and 2021, respectively. The United Nations World Tourism Organization [3] considered 2020 to be the worst year for the global tourism industry. Insofar, as the COVID-19 pandemic is severe and ongoing, forecasting tourism recovery accurately is urgently needed.Sentiment and mood have long been discussed in by economists and psychologists [4, 5] and are considered significant determinants of economic behavior and decision-making [6, 7]. Travel sentiment, as the net transmitters of the spillover impact of tourism demand, depends on expected and accidental events and varies over time. It is a powerful source of information and affects both the reputation and performance of the tourism industry [8]. In January 2021, the UNWTO conducted a study of travel sentiment and found that the prognosis for 2021 was a mix of both hope and worry [3]. Approximately 30% of the respondents believed that COVID-19 would worsen tourism development. When asked about their expectations for tourism recovery, 43% of respondents did not expect tourism to recover until 2023 and 41% thought it would take until 2024 or later. It was apparent that COVID-19 not only halted tourism development but also negatively impacted tourism sentiment, making tourism recovery even more difficult. Since the outbreak of the pandemic, tourists’ travel intentions, behavior, and psychological activities have been greatly impacted, and they are more susceptible to mood swings [9]. These changes in travel sentiment could also result in short-term reductions in demand for tourism services and confidence in the industry, which would be detrimental to the industry’s ability to recover from the pandemic. As a result, forecasting travel sentiment is critical for tourism recovery and growth.Because of their distinctive geographic landscapes and cultural traditions, several nations around the world have become popular tourist destinations. The UNWTO listed the top 10 tourist destinations as follows: China, France, Germany, Italy, Mexico, Spain, Thailand, Turkey, the United Kingdom, and the United States. Collectively, these countries received 1.03 billion visitors in 2019. However, among the top 10 destinations in 2020, China experienced the biggest drop in foreign visitor arrivals (80% lower than the year before), while Mexico experienced the least (46% lower). Although border restrictions played a role in the decline in tourist arrivals, uncertainty about the effects of the pandemic had a more significant impact on travel behavior. Fortunately, the outbreaks were contained or even averted in several countries thanks to the development, production, and administration of vaccines. This has allowed attitudes toward travel to gradually improve along with trust in tourism recovery. Because the pandemic and the vaccinations alter the tendency of the travel sentiment initial occurrence, both have had a shock effect on travel sentiment and tourism recovery. Therefore, measuring shock effects and forecasting travel sentiment is the top priority for the recovery of tourism recovery.Shock-disturbed system forecasting has always been a thorny problem in forecast science. The grey prediction model was proposed by Deng [10] and focused on uncertain issues with few data and little information. Grey prediction models employ an accumulative operation to weaken or eliminate the influence of shock disturbances on system behavior and hence achieve great forecasting performance [11–14]. The grey univariable prediction GM (1, 1) model and the grey multivariable prediction GM (1, N) model are the two most widely used grey prediction models. Numerous research studies used the GM (1, N) model to forecast while taking the effects of relevant elements into account because the GM (1, 1) model only reflects the sequence response to time [15]. Therefore, the GM (1, 1) model and GM (1, N) model are used to forecast the travel sentiment of the top 10 tourist destinations in the world in order to compare the travel sentiment without shock effect and with shock effect caused by COVID-19 and vaccination, respectively. In addition, this paper proposed a hybrid prediction model, denoted as F-GM (1, 1) and F-GM (1, N), which combined the original GM (1, 1) model and GM (1, N) model with Fourier series as the residual modification model as increasing prediction accuracy without affecting the original structure. Ultimately, a three-stage change process shock disturbance analysis mechanism is suggested in order to comprehend how COVID-19 and vaccination interact, as well as to predict future consequences from changes in the post-COVID-19 era.The remainder of the paper is arranged into the following sections. Related research is reviewed in Section2. Section 3 introduces the GM (1, 1) and GM (1, N) models, as well as the proposed F-GM (1, 1) and F-GM (1, N) models. Section 4 considers the shock effect of COVID-19 and vaccination to forecast travel sentiment in the top 10 tourist destinations. Section 5 concludes with a list of recommendations for further study in the field.


## 2. Literature Review

### 2.1. Travel Sentiment and Tourism

The requirement or situation that prompts a traveler to book a vacation that will likely satisfy a need or condition is known as the motive for travel [16]. Tourism motivation explains why people want to travel, the reason they choose their destination, and the particular activities they partake in while on vacation [17]. People’s motivations for traveling might have changed as a result of the pandemic’s negative effects [18], as external events or crises commonly alter these motives [19]. In the early pandemic, potential visitors tended to postpone their travel plans. Thereafter, itineraries were rearranged to be mindful of travelers’ new travel habits and perceived risks [20, 21]. A variety of surveys have been carried out globally to ascertain the factors influencing the selection of a destination, lodging, mode of transportation, and travel intention and the origins of so-called travel sentiment. Travel sentiment is described as the combination of travel intent, trip planning, and travel anxieties and represents tourists’ eagerness to travel [16]. Three dimensions, namely, travel intentions, trip planning, and travel concerns, were combined under the concept of travel sentiment [22–24]. According to empirical research conducted by Aharon [25], sentiment played a significant role in the tourist and leisure industries whereas macroeconomic considerations had minimal impact. Travel sentiment has been used with a focus on interpreting the causal factors pertaining to tourist development [26]. Many studies in the tourism and hospitality sectors have focused on travel sentiment analysis. These studies, however, focused on assessing the opinions posted by tourists on multiple platforms using sentiment analysis and opinion-mining techniques [27–29]. Because of this, despite their semantic similarity, the travel sentiment examined in this paper and the sentiment conveyed in reviews are not the same. It clarifies the true willingness to travel, nevertheless. Therefore, this paper’s attempt to increase the forecasting accuracy of travel sentiment aims to promote tourism while also attempting to understand how travel sentiment changed during the COVID-19 outbreak.


### 2.2. Shock Effects of COVID-19 and Vaccination on Tourism and Travel Sentiment

The tourist industry was among those most adversely affected by the COVID-19 outbreak due to various restrictions on land, sea, and air links for leisure travel [30]. The pandemic had a catastrophic effect on the GDP and employment in the travel and tourist industry, resulting in costs up to 2.1 trillion USD and a loss of 62 million jobs with a fall of 18.5% in 2020 [31, 32]. As highlighted by Abdullah et al. [20], several limitations were put in place for travelers throughout the previous two years by various nations to stop or limit the spread of the virus. Vacationers, therefore, had to stay inside and get used to a new, “forced” reality rather than leaving their homes and enjoying their time away as normal [16, 33]. On the other hand, numerous research studies revealed that although COVID-19 had seriously affected international tourism in terms of numbers of trips and tourist behavior and sentiments, travelers have started to demand new tourism offerings [27, 34]. Particularly, tourists’ sentiment in virtual tourism dominates [35]. In addition, compensating consumption might improve travel sentiment when infectious diseases prevent travel [36].Travelers’ concerns are cited in the literature on travel medicine as one of the main factors contributing to their lack of vaccination [37–39]. As a result, a worldwide vaccination campaign is currently being carried out to lessen the effects of and protect individuals against the COVID-19 pandemic [40]. According to certain research, the COVID-19 vaccine could aid in resuming travel and boosting both domestic and foreign tourism [41, 42]. Williams et al. [43] found two COVID-19 vaccine confidence clusters, the high and the low confidence group. The high confidence group thought that the adoption of the vaccine would help to enhance tourism confidence and aid in the industry’s revival. In discussion of COVID-19 vaccination passports and COVID-19 vaccine tourism, Shin et al. [44] and Kaewkitipong et al. [45] came to the conclusion that both of these policies were crucial for the recovery of travel demand. Studies based on online social media websites like Twitter also discovered that vaccination improved travel attitudes by reviving travel confidence [40, 46, 47].Because of the immediacy, unpredictability, and volatility of crises like the COVID-19 pandemic, tourism and travel sentiment are unexpectedly shocked. Similarly, the administration of vaccines altered perceptions of the pandemic and affected tourism’s recovery capacity. Therefore, this paper aimed to effectively forecast travel sentiment by taking into account the shock effects of COVID-19 and vaccination.


### 2.3. Grey Prediction in Tourism Prediction

The grey prediction model is a key component of the grey system, a technique used to address the issue of incomplete and unclear information, and no statistical assumptions. The grey prediction model has the ability to directly transform a time series model into differential equations, creating a developed dynamic model of an abstract system [48]. As a result, several academics have widely used grey prediction models in a variety of domains, including population structure, energy consumption and demand, and Internet of things technology [49–52]. Because of these qualities, grey prediction models have been used in tourism, including tourism demand [53, 54], annual foreign tourist arrivals [55], and tourism volumes [56]. The grey prediction models have outperformed in tourism prediction. However, the grey multivariate prediction GM (1, N) model has not been utilized as much in the previous literature [57]. Furthermore, there are few studies available on predicting travel sentiment. Because travel sentiment influences the tourism recovery, it is crucial to precisely predict the trend in the post-COVID-19 era.Since accuracy is the foundation of the prediction model, multiple methods have been used to improve the accuracy, including modifying background values with fractional order accumulation, tectonic background value, and background value optimization [58–60]; integrating a grey wolf optimizer, genetic optimization algorithm, and fuzzy neural network for optimizing [61, 62]; and establishing a grey Bernoulli forecasting model and a nonlinear multivariable Verhulst grey prediction model to represent the characteristics of nonlinear [62, 63]. The accuracy of forecasts has improved due to abovementioned methods, however, at the expense of changing the local characteristics of the grey prediction model [64]. Therefore, the Markov-chain [65], Fourier series [66, 67], and neural network [68] were applied as residual modification models to increase the prediction capability.The Fourier series is a basis function that can expand any periodic function [69]. Furthermore, the residuals can be turned into frequency spectra using the Fourier series, which can filter out high-frequency terms and improve performance [70]. Consequently, the Fourier series has frequently been merged with a grey prediction model due to the improved performance achieved with a residual modification model. The primary goal of this paper is to increase prediction accuracy using a residual modification model without changing the initial parameters. As a result, this paper considered COVID-19 and vaccines while using the GM (1, 1) and GM (1, N) combined with Fourier series as residual modification model to forecast travel sentiment.


## 2.1. Travel Sentiment and Tourism

The requirement or situation that prompts a traveler to book a vacation that will likely satisfy a need or condition is known as the motive for travel [16]. Tourism motivation explains why people want to travel, the reason they choose their destination, and the particular activities they partake in while on vacation [17]. People’s motivations for traveling might have changed as a result of the pandemic’s negative effects [18], as external events or crises commonly alter these motives [19]. In the early pandemic, potential visitors tended to postpone their travel plans. Thereafter, itineraries were rearranged to be mindful of travelers’ new travel habits and perceived risks [20, 21]. A variety of surveys have been carried out globally to ascertain the factors influencing the selection of a destination, lodging, mode of transportation, and travel intention and the origins of so-called travel sentiment. Travel sentiment is described as the combination of travel intent, trip planning, and travel anxieties and represents tourists’ eagerness to travel [16]. Three dimensions, namely, travel intentions, trip planning, and travel concerns, were combined under the concept of travel sentiment [22–24]. According to empirical research conducted by Aharon [25], sentiment played a significant role in the tourist and leisure industries whereas macroeconomic considerations had minimal impact. Travel sentiment has been used with a focus on interpreting the causal factors pertaining to tourist development [26]. Many studies in the tourism and hospitality sectors have focused on travel sentiment analysis. These studies, however, focused on assessing the opinions posted by tourists on multiple platforms using sentiment analysis and opinion-mining techniques [27–29]. Because of this, despite their semantic similarity, the travel sentiment examined in this paper and the sentiment conveyed in reviews are not the same. It clarifies the true willingness to travel, nevertheless. Therefore, this paper’s attempt to increase the forecasting accuracy of travel sentiment aims to promote tourism while also attempting to understand how travel sentiment changed during the COVID-19 outbreak.


## 2.2. Shock Effects of COVID-19 and Vaccination on Tourism and Travel Sentiment

The tourist industry was among those most adversely affected by the COVID-19 outbreak due to various restrictions on land, sea, and air links for leisure travel [30]. The pandemic had a catastrophic effect on the GDP and employment in the travel and tourist industry, resulting in costs up to 2.1 trillion USD and a loss of 62 million jobs with a fall of 18.5% in 2020 [31, 32]. As highlighted by Abdullah et al. [20], several limitations were put in place for travelers throughout the previous two years by various nations to stop or limit the spread of the virus. Vacationers, therefore, had to stay inside and get used to a new, “forced” reality rather than leaving their homes and enjoying their time away as normal [16, 33]. On the other hand, numerous research studies revealed that although COVID-19 had seriously affected international tourism in terms of numbers of trips and tourist behavior and sentiments, travelers have started to demand new tourism offerings [27, 34]. Particularly, tourists’ sentiment in virtual tourism dominates [35]. In addition, compensating consumption might improve travel sentiment when infectious diseases prevent travel [36].Travelers’ concerns are cited in the literature on travel medicine as one of the main factors contributing to their lack of vaccination [37–39]. As a result, a worldwide vaccination campaign is currently being carried out to lessen the effects of and protect individuals against the COVID-19 pandemic [40]. According to certain research, the COVID-19 vaccine could aid in resuming travel and boosting both domestic and foreign tourism [41, 42]. Williams et al. [43] found two COVID-19 vaccine confidence clusters, the high and the low confidence group. The high confidence group thought that the adoption of the vaccine would help to enhance tourism confidence and aid in the industry’s revival. In discussion of COVID-19 vaccination passports and COVID-19 vaccine tourism, Shin et al. [44] and Kaewkitipong et al. [45] came to the conclusion that both of these policies were crucial for the recovery of travel demand. Studies based on online social media websites like Twitter also discovered that vaccination improved travel attitudes by reviving travel confidence [40, 46, 47].Because of the immediacy, unpredictability, and volatility of crises like the COVID-19 pandemic, tourism and travel sentiment are unexpectedly shocked. Similarly, the administration of vaccines altered perceptions of the pandemic and affected tourism’s recovery capacity. Therefore, this paper aimed to effectively forecast travel sentiment by taking into account the shock effects of COVID-19 and vaccination.


## 2.3. Grey Prediction in Tourism Prediction

The grey prediction model is a key component of the grey system, a technique used to address the issue of incomplete and unclear information, and no statistical assumptions. The grey prediction model has the ability to directly transform a time series model into differential equations, creating a developed dynamic model of an abstract system [48]. As a result, several academics have widely used grey prediction models in a variety of domains, including population structure, energy consumption and demand, and Internet of things technology [49–52]. Because of these qualities, grey prediction models have been used in tourism, including tourism demand [53, 54], annual foreign tourist arrivals [55], and tourism volumes [56]. The grey prediction models have outperformed in tourism prediction. However, the grey multivariate prediction GM (1, N) model has not been utilized as much in the previous literature [57]. Furthermore, there are few studies available on predicting travel sentiment. Because travel sentiment influences the tourism recovery, it is crucial to precisely predict the trend in the post-COVID-19 era.Since accuracy is the foundation of the prediction model, multiple methods have been used to improve the accuracy, including modifying background values with fractional order accumulation, tectonic background value, and background value optimization [58–60]; integrating a grey wolf optimizer, genetic optimization algorithm, and fuzzy neural network for optimizing [61, 62]; and establishing a grey Bernoulli forecasting model and a nonlinear multivariable Verhulst grey prediction model to represent the characteristics of nonlinear [62, 63]. The accuracy of forecasts has improved due to abovementioned methods, however, at the expense of changing the local characteristics of the grey prediction model [64]. Therefore, the Markov-chain [65], Fourier series [66, 67], and neural network [68] were applied as residual modification models to increase the prediction capability.The Fourier series is a basis function that can expand any periodic function [69]. Furthermore, the residuals can be turned into frequency spectra using the Fourier series, which can filter out high-frequency terms and improve performance [70]. Consequently, the Fourier series has frequently been merged with a grey prediction model due to the improved performance achieved with a residual modification model. The primary goal of this paper is to increase prediction accuracy using a residual modification model without changing the initial parameters. As a result, this paper considered COVID-19 and vaccines while using the GM (1, 1) and GM (1, N) combined with Fourier series as residual modification model to forecast travel sentiment.


## 3. Methodologies

### 3.1. GM (1, 1) Model

The grey prediction model was established by Ju-Long [71], which could be divided into two models, namely, GM (1, 1) model and GM (1, N) model. The GM (1, 1) model was a “one order one variable” grey univariable prediction model compatible with the grey differentiation and time-varying difference. The computational steps to construct a GM (1, 1) model are as follows.Assume thatX0=x01,x02,…,x0n is an original and nonnegative data sequence consisting of n samples. Then, generate a new sequence X1=x11,x12,…,x1n by performing the accumulated generating operation (AGO), which can identify the potential regularity hidden in X0.(1)x1k=∑j=1kx1j,k=1,2,…,n,and x1k,x1k,…,x1k can be then approximated by a first-order differential equation:(2)dx1dt+ax1=b,where a and b are the developing coefficient and control variable, respectively. The predicted value, x^1k, for x1k can be obtained by solving the differential equation with initial condition x11=x01:(3)x^1k=x01−bae−ak−1+ba.The developing coefficienta and control variable b can be obtained using the ordinary least-square (OLS) methods as follows:(4)a,bT=BTB−1BTy,where(5)B=−z121−z131⋮⋮−z1n1,z1k=αx1k+1−αx1k−1,y=x02,x03,...,x0nT,where z1k is the background value. α is usually specified as 0.5.Performing the inverse accumulated generating operation (IAGO), the predicted value orx0k is(6)x^0k=x^1k−x^1k−1,k=2,3,…,n.Therefore,(7)x^0k=1−eax01−bae−ak−1,k=2,3,…,n,and note that x11=x01 holds.


### 3.2. GM (1,N) Model

The GM (1,N) model is a first-order grey multivariable prediction model with N variables [72]. The inclusion of relevant variables in the prediction model is the main characteristic of the GM (1, N) model. Consequently, it is more useful than a grey forecasting model with a single variable for simulating the system’s operating rules and development tendency [73].Assume thatX10=x101,x102,…,x10n is a sequence of original data of a system characteristic sequence (or dependent variable sequence) and Xi0=xi01,xi02,…,xi0n, where i=2,3,…,N is the explanatory variable sequences (or independent variable sequences), which have a certain relationship with sequence X10.Then, the new sequenceXi0=xi01,xi02,…,xi0n can be generated from X10 by the accumulated generating operation as follows:(8)xi1k=∑j=1kxi0j,k=1,2,…,n,and x111,x112,…,x11n can then be approximated by a first-order differential equation as follows:(9)dx11dt+ax11=∑i=2nbixi1,where a is called the development coefficient of the system and bixi1k and bi are the driving term and driving coefficient, respectively.The predicted valuex^i1k can be obtained by solving the differential equation with an initial condition that x111=x111:(10)x^11k=x101−1a∑i=2nbixi1ke−ak−1+1a∑i=2nbixi1k,and thus x^111=x101 holds.Then,a and bi can be estimated by a grey difference equation:(11)x10k+az11k=∑i=2nbixi1k,where z11k the background value, is the adjacent neighbor mean generated sequence of X11,(12)z11k=αx11k+1−αx11k−1,and α is usually specified as 0.5. In turn, a and bi can be obtained using the OLS:(13)a,biT=BTB−1BTy,B=−z112x212⋯xN12−z113x113⋯xN13⋮⋮⋱⋮−z11nx21n⋯xN1n,y=x102,x103,…,x10nT.Using the inverse accumulated generating operation, the predicted valuexk0 is(14)x^10k=x^11k−x^11k−1,k=2,3,…,n.Note thatx^111=x101 holds.


### 3.3. Residual Modification Model

According to the literature review, the grey prediction models are frequently used because they are appropriate for small samples and insufficient data, and they can weaken the randomness of original time series by AGOs. However, there are several flaws in both the GM (1, 1) model and the GM (1,N) model that could reduce forecast accuracy. When it comes to the GM (1, 1) model, the model has a weak capacity for predicting nonlinear and nonstationary time series [65]. The solution of the whitening differential equation for the GM (1, N) model is rough and can easily result in large errors in actual forecasting applications [66]. The residual modification model is proposed to further increase the existing grey prediction models’ prediction accuracy.The Fourier series was used as a residual modification model in combination with the original GM (1, 1) and GM (1,N) models to establish the F-GM (1, 1) and F-GM (1, N) models, in order to increase prediction accuracy. The low-frequency term will be selected after the Fourier series transform the residuals error of GM (1, 1) and GM (1, N) models into frequency spectra. This can improve performance by filtering out high-frequency terms, which are thought to be noisy. The following are the computational procedures for creating a residual modification model using Fourier series:Step 1.
Generate the sequence of residual values,ε0k=ε02,ε03,…,ε0n.
Expressed in Fourier series,ε0k is rewritten as follows:(15)ε0k=12a0+∑i=1Faicos2πin−1k+bisin2πin−1k,k=2,3,…,n,where F=n−1/2−1 is called the minimum deployment frequency of Fourier series and only take integer number [74]. Therefore, the residual series is rewritten as follows:(16)ε0=PC,where(17)P=12cos2π×1n−1×3sin2π×1n−1×2⋯cos2π×Fn−1×2sin2π×Fn−1×212cos2π×1n−1×2sin2π×1n−1×3⋯cos2π×Fn−1×3sin2π×Fn−1×3⋮⋮⋮⋱⋮⋮12cos2π×1n−1×nsin2π×1n−1×n⋯cos2π×Fn−1×nsin2π×Fn−1×n,C=a0,a1,b1,a2,b2,…,aF,bFT.
The parametersa0,a1,b1,a2,b2,…,aF,bF are obtained by using the ordinary least-squares method that results in the following equation:(18)C=PTP−1PTε0T.
Once the parameters are calculated, the predicted residualε^0k is then easily achieved based on the following expression:(19)ε^0k=12a0+∑i=1Fa^icos2πin−1k+b^isin2πin−1k.
The predicted value of F-GM (1,N), x˜10k from the GM (1, N) model can be calculated as follows:(20)x˜0k=x^0k+ε^0k,k=2,3,…,n.
Note thatx˜01=x01 holds.


### 3.4. Evaluating Prediction Accuracy

The predicting performance of the suggested models was compared to other models in this study using the mean absolute percentage error (MAPE). MAPE with respect tox0k is as follows:(21)MAPE=1n∑k=1nx0k−x^0kx0k.Lewis [75] found that the MAPE ≤ 10%, 10% < MAPE ≤ 20%, 20% < MAPE ≤ 50%, and MAPE > 50, respectively, reflected the high, good, fair, and weak forecasting models.


## 3.1. GM (1, 1) Model

The grey prediction model was established by Ju-Long [71], which could be divided into two models, namely, GM (1, 1) model and GM (1, N) model. The GM (1, 1) model was a “one order one variable” grey univariable prediction model compatible with the grey differentiation and time-varying difference. The computational steps to construct a GM (1, 1) model are as follows.Assume thatX0=x01,x02,…,x0n is an original and nonnegative data sequence consisting of n samples. Then, generate a new sequence X1=x11,x12,…,x1n by performing the accumulated generating operation (AGO), which can identify the potential regularity hidden in X0.(1)x1k=∑j=1kx1j,k=1,2,…,n,and x1k,x1k,…,x1k can be then approximated by a first-order differential equation:(2)dx1dt+ax1=b,where a and b are the developing coefficient and control variable, respectively. The predicted value, x^1k, for x1k can be obtained by solving the differential equation with initial condition x11=x01:(3)x^1k=x01−bae−ak−1+ba.The developing coefficienta and control variable b can be obtained using the ordinary least-square (OLS) methods as follows:(4)a,bT=BTB−1BTy,where(5)B=−z121−z131⋮⋮−z1n1,z1k=αx1k+1−αx1k−1,y=x02,x03,...,x0nT,where z1k is the background value. α is usually specified as 0.5.Performing the inverse accumulated generating operation (IAGO), the predicted value orx0k is(6)x^0k=x^1k−x^1k−1,k=2,3,…,n.Therefore,(7)x^0k=1−eax01−bae−ak−1,k=2,3,…,n,and note that x11=x01 holds.


## 3.2. GM (1,N) Model

The GM (1,N) model is a first-order grey multivariable prediction model with N variables [72]. The inclusion of relevant variables in the prediction model is the main characteristic of the GM (1, N) model. Consequently, it is more useful than a grey forecasting model with a single variable for simulating the system’s operating rules and development tendency [73].Assume thatX10=x101,x102,…,x10n is a sequence of original data of a system characteristic sequence (or dependent variable sequence) and Xi0=xi01,xi02,…,xi0n, where i=2,3,…,N is the explanatory variable sequences (or independent variable sequences), which have a certain relationship with sequence X10.Then, the new sequenceXi0=xi01,xi02,…,xi0n can be generated from X10 by the accumulated generating operation as follows:(8)xi1k=∑j=1kxi0j,k=1,2,…,n,and x111,x112,…,x11n can then be approximated by a first-order differential equation as follows:(9)dx11dt+ax11=∑i=2nbixi1,where a is called the development coefficient of the system and bixi1k and bi are the driving term and driving coefficient, respectively.The predicted valuex^i1k can be obtained by solving the differential equation with an initial condition that x111=x111:(10)x^11k=x101−1a∑i=2nbixi1ke−ak−1+1a∑i=2nbixi1k,and thus x^111=x101 holds.Then,a and bi can be estimated by a grey difference equation:(11)x10k+az11k=∑i=2nbixi1k,where z11k the background value, is the adjacent neighbor mean generated sequence of X11,(12)z11k=αx11k+1−αx11k−1,and α is usually specified as 0.5. In turn, a and bi can be obtained using the OLS:(13)a,biT=BTB−1BTy,B=−z112x212⋯xN12−z113x113⋯xN13⋮⋮⋱⋮−z11nx21n⋯xN1n,y=x102,x103,…,x10nT.Using the inverse accumulated generating operation, the predicted valuexk0 is(14)x^10k=x^11k−x^11k−1,k=2,3,…,n.Note thatx^111=x101 holds.


## 3.3. Residual Modification Model

According to the literature review, the grey prediction models are frequently used because they are appropriate for small samples and insufficient data, and they can weaken the randomness of original time series by AGOs. However, there are several flaws in both the GM (1, 1) model and the GM (1,N) model that could reduce forecast accuracy. When it comes to the GM (1, 1) model, the model has a weak capacity for predicting nonlinear and nonstationary time series [65]. The solution of the whitening differential equation for the GM (1, N) model is rough and can easily result in large errors in actual forecasting applications [66]. The residual modification model is proposed to further increase the existing grey prediction models’ prediction accuracy.The Fourier series was used as a residual modification model in combination with the original GM (1, 1) and GM (1,N) models to establish the F-GM (1, 1) and F-GM (1, N) models, in order to increase prediction accuracy. The low-frequency term will be selected after the Fourier series transform the residuals error of GM (1, 1) and GM (1, N) models into frequency spectra. This can improve performance by filtering out high-frequency terms, which are thought to be noisy. The following are the computational procedures for creating a residual modification model using Fourier series:Step 1.
Generate the sequence of residual values,ε0k=ε02,ε03,…,ε0n.
Expressed in Fourier series,ε0k is rewritten as follows:(15)ε0k=12a0+∑i=1Faicos2πin−1k+bisin2πin−1k,k=2,3,…,n,where F=n−1/2−1 is called the minimum deployment frequency of Fourier series and only take integer number [74]. Therefore, the residual series is rewritten as follows:(16)ε0=PC,where(17)P=12cos2π×1n−1×3sin2π×1n−1×2⋯cos2π×Fn−1×2sin2π×Fn−1×212cos2π×1n−1×2sin2π×1n−1×3⋯cos2π×Fn−1×3sin2π×Fn−1×3⋮⋮⋮⋱⋮⋮12cos2π×1n−1×nsin2π×1n−1×n⋯cos2π×Fn−1×nsin2π×Fn−1×n,C=a0,a1,b1,a2,b2,…,aF,bFT.
The parametersa0,a1,b1,a2,b2,…,aF,bF are obtained by using the ordinary least-squares method that results in the following equation:(18)C=PTP−1PTε0T.
Once the parameters are calculated, the predicted residualε^0k is then easily achieved based on the following expression:(19)ε^0k=12a0+∑i=1Fa^icos2πin−1k+b^isin2πin−1k.
The predicted value of F-GM (1,N), x˜10k from the GM (1, N) model can be calculated as follows:(20)x˜0k=x^0k+ε^0k,k=2,3,…,n.
Note thatx˜01=x01 holds.


## 3.4. Evaluating Prediction Accuracy

The predicting performance of the suggested models was compared to other models in this study using the mean absolute percentage error (MAPE). MAPE with respect tox0k is as follows:(21)MAPE=1n∑k=1nx0k−x^0kx0k.Lewis [75] found that the MAPE ≤ 10%, 10% < MAPE ≤ 20%, 20% < MAPE ≤ 50%, and MAPE > 50, respectively, reflected the high, good, fair, and weak forecasting models.


## 4. Empirical Study

### 4.1. Comparative Analysis of the Shock Effects of COVID-19 and Vaccination

The development tendency and prediction accuracy of the system will be significantly influenced by past performance, development features, and the relative influencing factors. In order to examine the shock effects of COVID-19 and vaccination as relevant factors, this paper used the original GM (1, 1) and GM (1,N) models as well as the proposed F-GM (1, 1) and F-GM (1, N) models provided in Section 3 to forecast travel sentiment globally and in the top 10 destinations. The entire procedure can be broken down into three phases: the no-epidemic phase, the phase of COVID-19 outbreaks, and the phase of COVID-19 vaccination coexistence. In Phase I, without pandemic shock, the previous developing trend in travel sentiment will persist. Therefore, the GM (1, 1) and F-GM (1, 1) models were used to predict travel sentiment by simply accounting for the temporal effects.If a shock is introduced into a system at a specific time, the impact will cause the initial trend to shift. The global alarm over the pandemic, which had a significant impact on travel sentiment, was exacerbated by the rise in the overall cases of COVID-19. Tourists’ strong disapproval of tourism growth may further depress travel sentiment. In order to forecast travel sentiment, COVID-19 was added as a relevant variable to the GM (1,N) model and F-GM (1, N) model in Phase II.To further assess and forecast travel sentiment, the shock effects of the COVID-19 and vaccination are considered simultaneously in Phase III. In several countries, the pandemic was successfully controlled once COVID-19 vaccines were developed, produced, and administered. Citizens’ confidence in tourism would return as a result, potentially increasing travel sentiment. On the premise of maintaining the relevant variable of the COVID-19 as constant, the paper introduced the vaccination as a relevant variable in the GM (1,N) and the F-GM (1, N) model to predict travel sentiment in Phase III.


### 4.2. Data Collection

The duration of the data differs among the top 10 destinations, due to the varying timing of COVID-19 confirmation and the lengthy procedure involved in vaccine research, development, and administration. Travel sentiment was represented using the monthly net sentiment scores from the UNWTO Tourism Recovery Tracker. COVID-19 and vaccine data, which were represented by the monthly COVID-19 cases per million and monthly vaccinations per hundred, respectively, were derived from Our World in Data. Data from each country’s beginning month through September 2022 were reserved for model fitting, and the data from October to November 2022 were reserved for ex-post testing. Table1 displays the data lengths for various countries.Table 1
The length of the data.
NationsTravel sentimentsCOVID-19 casesVaccinationsWorld, China, Germany, Italy, USJan. 2020–Nov. 2022Jan. 2020–Nov. 2022Dec. 2020–Nov. 2022France, UKJan. 2020–Nov. 2022Jan. 2020–Nov. 2022Jan. 2020–Nov. 2022MexicoJan. 2020–Nov. 2022Feb. 2020–Nov. 2022Dec. 2020–Nov. 2022SpainJan. 2020–Nov. 2022Feb. 2020–Nov. 2022Jan. 2020–Nov. 2022ThailandJan. 2020–Nov. 2022Jan. 2020–Nov. 2022Mar. 2020–Nov. 2022TurkeyJan. 2020–Nov. 2022Mar. 2020–Nov. 2022Jan. 2020–Nov. 2022


### 4.3. Predictive Analysis of Travel Sentiment

Because of the large number of countries and the similar analysis process, this paper used global travel sentiment prediction as an example to analyze the shock effects of COVID-19 and vaccination by following the computation steps in Section3. The prediction results of global travel sentiment are shown in Table 2. In more detail, the MAPE of the GM (1, 1), F-GM (1, 1), GM (1, N), and F-GM (1, N) models for model fitting in Phase I, II, and III is 3.53%, 0.86%, 21.14%, 1.48%, 23.86%, and 1.56%, respectively. The MAPE is 2.68%, 8.14%, 25.16%, 24.88%, 11.57%, and 6.52%, respectively, for ex-post testing. When shock effects are not introduced in Phase I, the MAPE of the F-GM (1, 1) model is better for model fitting than the GM (1, 1) model, but the F-GM (1, 1) model is worse for ex-post testing. The F-GM (1, N) model, which combined the residual modification model, outperformed the GM (1, 1) model in the Phase II and III, both in terms of model fitting and ex-post testing. Beyond all doubt, the grey prediction model integrated with modification model would improve the prediction accuracy.Table 2
Forecasting results of the competing models for global travel sentiment.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 202033.0033.000.0033.000.0033.000.0033.000.00Feb. 202030.0024.484.2428.820.9119.148.3532.021.55Mar. 202010.0024.9913.6311.181.0720.569.607.981.84Apr. 202019.0025.515.4717.820.9921.722.2921.021.70May. 202024.0026.021.6325.180.9522.880.9021.981.63Jun. 202025.0026.541.2323.820.9423.711.0327.021.62Jul. 202025.0027.061.6426.180.9423.820.9422.981.62Aug. 202027.0027.580.4525.820.9324.242.1729.021.59Sep. 202034.0028.104.4035.180.8824.646.9931.981.51Oct. 202031.0028.621.8129.820.9023.335.8533.021.54Nov. 202038.0029.156.4139.180.8520.4612.7135.981.46Dec. 202040.0029.687.3738.820.8417.9415.7642.021.4440.000.0040.000.00Jan. 202123.0030.215.8624.180.9617.584.4020.981.6424.231.0022.190.66Feb. 202128.0030.742.1426.820.9223.153.7930.021.5840.9410.1128.800.63Mar. 202128.0031.282.5629.180.9220.395.9425.981.5854.3720.6027.220.61Apr. 202131.0031.820.6229.820.9013.0613.6933.021.5464.4825.5631.740.56May. 202132.0032.360.2733.180.8914.8413.0029.981.5374.2332.0031.320.52Jun. 202134.0032.900.8232.820.8822.108.8836.021.5184.3637.5834.610.45Jul. 202131.0033.441.8732.180.9017.5410.2728.981.5487.2842.9630.480.40Aug. 202130.0033.993.0728.820.9112.0813.7932.021.5590.6246.6330.420.32Sep. 202135.0034.540.3436.180.8715.7714.2532.981.5089.7240.5334.690.23Oct. 202144.0035.096.1942.820.8219.1017.2946.021.4088.7931.1044.200.14Nov. 202145.0035.646.4546.180.8115.3420.4542.981.3989.5330.7144.920.06Dec. 202150.0036.209.2048.820.790.0833.2852.021.3588.5225.6849.960.03Jan. 202237.0036.760.1838.180.86−101.97101.4434.981.4768.6723.1237.160.12Feb. 202239.0037.321.2137.820.85−61.7272.4641.021.4570.8322.9038.720.20Mar. 202241.0037.882.2142.180.84−57.7670.0438.981.4367.0818.5041.390.27Apr. 202241.0038.441.8139.820.84−17.1141.2143.021.4368.0819.2140.510.35May. 202241.0039.011.4142.180.84−3.0031.2038.981.4366.6918.2241.580.41Jun. 202240.0039.580.3038.820.84−7.1233.6642.021.4464.4017.4339.340.47Jul. 202229.0040.158.6530.180.91−32.1647.4126.981.5759.1023.3329.720.56Aug. 202229.0040.739.0927.820.91−27.2143.5731.021.5757.6622.2255.6320.64Sep. 202236.0041.303.9037.180.87−6.0430.9133.981.4857.2215.6145.096.68MAPE (%)3.530.8621.141.4823.861.56Oct. 202236.0041.884.3346.227.518.6320.1321.5010.6655.6114.4253.5712.92Nov. 202241.0042.461.0428.658.76−1.5630.19−14.1439.1153.308.7341.170.12MAPE (%)2.688.1425.1624.8811.576.52To further forecast global travel sentiment, the GM (1, 1) model is used to predict the relevant variables from December 2022 through February 2023. The results are displayed in Table3, showing that the total cases per million of COVID-19 remained on the rise in 2022 and 2023 while many countries adopted strict prevention and quarantine measures and even the complete border closures. In addition, it is worth noting that most people believe that vaccines are one of the best methods against the COVID-19. The future vaccination concentration rate has decreased slightly but is otherwise basically identical.Table 3
Prediction of relevant variables.
DatesCOVID-19VaccinationsDec. 20222148.324.90Jan. 20233252.114.76Feb. 20233272.484.62The predicted values of COVID-19 and vaccination are substituted into the GM models with a residual modification model to further forecast global travel sentiment. Table4 shows the forecasting of global travel sentiment for the different phases. Also, the actual values and predicted values obtained by the different models are intuitively displayed in Figure 1. It is very obvious from Figure 1 that the prediction of travel sentiment varies among the different models. More specifically, under the influence of previous travel sentiment, Phase I, although the travel sentiment fluctuated, it remained stable, with a small decline in February 2023. After introducing the shock effects of COVID-19 (Phase II), on the one hand, the model can fit the actual value well. However, on the other hand, the out-of-sample prediction of travel sentiment showed a downward trend. This can be interpreted as showing that the negative sentiment of global tourists is still high, that they believe that tourism is still seriously affected by the pandemic, and that they are not confident in tourism recovery. The shock effects of the pandemic and the vaccine are included in Phase III. The extrapolated findings show that travel sentiment has gradually declined along with the drop in the vaccination proportion. However, the travel sentiment is still positive, showing that tourists are growing more confident in the tourism. To a certain extent, the prediction results prove the effectiveness of pandemic measures and the correctness of vaccination.Table 4
Predicted travel sentiment in different countries.
DatesPhase IPhase IIPhase IIIDec. 202235.36−14.2724.12Jan. 202342.79−51.6618.26Feb. 202341.51−53.676.44Figure 1
Global travel sentiment predictions from Jan. 2020 to Jun. 2022.Phase III includes the vaccines and the pandemic’s shock effects.For details of the actual values and predicted values of travel sentiment for the top 10 destinations, refer to Tables5–14. Except for Thailand (see Table 11), which has consistently maintained a high level of travel sentiment, China (see Table 5) and Turkey (see Table 12) have experienced significant fluctuations among the three Asian nations. Future trends show an upward tendency for Turkey but a declining trend for Thailand and China. In contrast to the Asian nations, the sample data indicate that the five European countries of France (see Table 6), Germany (see Table 7), Italy (see Table 8), Spain (see Table 10), and the UK (see Table 13) have a rather positive overall travel sentiment. Due to the unpredictability and frequent outbreaks of the COVID-19, travel sentiment will similarly move negatively in the upcoming months as it does in Asian countries. The US (see Table 14) and Mexico (see Table 9), two countries in the Americas, both experienced a through in traveler sentiment in January 2021 before slowly rebounding.Table 5
Prediction results of travel sentiment in China.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 2020−56.00−56.000.00−56.000.00−56.000.00−56.000.00Feb. 2020−66.00−40.4775.10−66.100.30−39.7277.29−66.692.02Mar. 2020−74.00−38.92134.91−73.900.39−38.53136.43−73.312.64Apr. 2020−79.00−37.34198.37−79.100.48−37.30198.57−79.693.27May. 2020−57.00−35.7249.49−56.900.23−36.0348.76−56.311.60Jun. 2020−44.00−34.0517.76−44.100.18−34.7416.53−44.691.23Jul. 2020−52.00−32.3540.95−51.900.21−33.4338.69−51.311.43Aug. 2020−36.00−30.598.45−36.100.16−32.096.11−36.691.07Sep. 2020−56.00−28.7961.83−55.900.23−30.7157.48−55.311.56Oct. 2020−50.00−26.9546.10−50.100.20−29.3141.38−50.691.37Nov. 2020−5.00−25.0621.11−4.900.11−27.8724.07−4.310.72Dec. 2020−20.00−23.123.89−20.100.13−26.397.99−20.690.86−20.000.00−20.000.00Jan. 2021−24.00−21.123.78−23.900.13−24.971.28−23.310.90−8.0221.02−26.583.39Feb. 2021−10.00−19.0810.09−10.100.11−23.3614.85−10.690.767.3719.30−8.341.84Mar. 20210.00−16.9816.980.100.10−21.7921.790.690.6920.0520.05−0.700.70Apr. 202119.00−14.8328.4318.900.08−20.2032.9418.310.5832.1311.0318.730.23May. 202115.00−12.6324.0215.100.09−18.5629.1915.690.6051.6931.9016.231.07Jun. 202122.00−10.3626.5321.900.08−16.9031.8921.310.5669.9439.3019.831.78Jul. 202117.00−8.0421.4017.100.09−15.2227.5417.690.5966.8542.6120.062.61Aug. 2021−7.00−5.661.44−7.100.11−13.527.01−7.690.7470.7683.62−10.884.17Sep. 202124.00−3.2221.9524.100.08−11.7028.7924.690.5554.4524.5628.613.72Oct. 202138.00−0.7128.0537.900.07−9.8834.7037.310.5047.857.1432.763.80Nov. 202112.001.869.0512.100.09−8.0617.9112.690.6158.8441.8217.765.14Dec. 202119.004.5012.1818.900.08−6.2921.2518.310.5864.6238.3412.865.16Jan. 202225.007.2114.2325.100.08−4.4323.5425.690.5550.5520.4431.395.11Feb. 202233.009.9917.3032.900.08−2.4626.6632.310.5245.749.5826.514.88Mar. 20221.0012.8411.721.100.10−7.638.551.690.6828.7627.497.456.39Apr. 20223.0015.7612.392.900.10−43.2044.852.310.67−57.7959.02−3.276.09May. 20228.0018.769.968.100.09−4.6611.728.690.6418.8410.0413.955.51Jun. 202217.0021.844.1316.900.092.5712.3316.310.5926.678.2711.514.69Jul. 2022−2.0024.9927.54−1.900.103.515.63−1.310.7022.7225.222.915.01Aug. 2022−26.0028.2373.28−26.100.142.3938.37−26.690.9314.2954.44−30.225.70Sep. 202215.0031.5514.3915.100.095.678.1115.690.6014.840.1318.442.99MAPE (%)31.720.1433.400.9527.063.64Oct. 202218.0034.9614.379.337.356.879.43−20.1032.2912.035.06−6.5220.78Nov. 202215.0038.4620.403.4810.02−3.4216.02−38.2046.265.768.04−9.9521.70MAPE (%)17.398.6812.7339.286.5521.24Dec. 202242.040.28−4.07−46.462.63−18.13Jan. 202345.7224.54−5.06−25.34−0.49−13.88Feb. 202349.5039.45−6.42−16.36−3.59−39.05Table 6
Prediction results of travel sentiment in France.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 202032.0032.000.0032.000.0032.000.0032.000.00Feb. 202024.0025.050.8422.151.4923.630.3023.120.71Mar. 2020−9.0025.5337.95−7.152.0324.3136.60−8.120.96Apr. 202034.0026.025.9632.151.3824.956.7633.120.65May. 202025.0026.501.2026.851.4825.680.5425.880.70Jun. 202037.0026.997.3035.151.3526.397.7536.120.64Jul. 202040.0027.498.9441.851.3227.089.2340.880.63Aug. 202019.0027.987.5517.151.5527.697.3018.120.74Sep. 202025.0028.472.7826.851.4828.052.4425.880.70Oct. 202017.0028.9710.2315.151.5827.709.1416.120.75Nov. 202045.0029.4710.7146.851.2827.9811.7445.880.60Dec. 202028.0029.971.5426.151.4529.381.0827.120.68Jan. 202135.0030.483.3536.851.3729.504.0735.880.6535.000.0035.000.00Feb. 202141.0030.987.1139.151.3130.047.7740.120.6240.152.0636.2711.55Mar. 202140.0031.496.0841.851.3229.577.4540.880.6340.250.6344.7311.83Apr. 202135.0032.002.2333.151.3729.673.9534.120.6541.6719.0730.2713.53May. 202139.0032.514.6740.851.3333.094.2539.880.6340.032.6543.7312.14Jun. 202143.0033.026.9841.151.2933.616.5742.120.6141.224.1438.2711.01Jul. 202115.0033.5316.1216.851.6133.3915.9915.880.7643.56190.4019.7331.56Aug. 202132.0034.051.5530.151.4032.900.6831.120.6642.3232.2427.2714.79Sep. 202118.0034.5714.0419.851.5734.9114.3318.880.7434.8593.6022.7326.30Oct. 202152.0035.0911.1250.151.2236.0510.4951.120.5830.5741.2147.279.10Nov. 202137.0035.611.0138.851.3535.081.4037.880.6433.688.9841.7312.79Dec. 202126.0036.148.0524.151.4726.810.6425.120.7057.73122.0221.2718.21Jan. 202233.0036.672.7634.851.39−8.9631.5533.880.66119.03260.6937.7314.35Feb. 202236.0037.200.8834.151.3617.8713.3335.120.6463.0375.0831.2713.15Mar. 202256.0037.7311.7157.851.1920.6322.6856.880.5654.293.0660.738.45Apr. 202252.0038.269.0450.151.2219.3521.4851.120.5855.546.8047.279.10May. 202257.0038.7911.6058.851.1831.8316.0357.880.5632.2643.4061.738.31Jun. 202250.0039.337.1148.151.2327.7814.8149.120.5838.9122.1845.279.47Jul. 202210.0039.8727.1611.851.6820.389.4410.880.8051.86418.5714.7347.34Aug. 202225.0040.4112.3323.151.4834.567.6424.120.7024.153.4120.2718.94Sep. 202234.0040.965.1935.851.3832.870.8434.880.6527.1620.1338.7313.92MAPE (%)8.031.379.340.6565.2515.04Oct. 202239.0041.501.8038.600.2829.187.0628.687.4342.057.8238.162.15Nov. 202240.0042.051.469.3721.8832.365.46−0.0728.6241.854.6246.3315.83MAPE (%)1.6311.086.2618.026.228.99Dec. 202242.6048.7329.4737.6541.7030.29Jan. 202343.1543.5019.3219.5241.6145.31Feb. 202343.7151.8617.8027.5441.5838.63Table 7
Prediction results of travel sentiment in Germany.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 202022.0022.000.0022.000.0022.000.0022.000.00Feb. 202018.0012.424.7318.800.685.9110.2421.763.18Mar. 2020−12.0013.0828.50−12.800.917.2621.88−15.764.27Apr. 202011.0013.742.4711.800.728.512.2414.763.39May. 20209.0014.414.968.200.7310.131.035.243.45Jun. 20209.0015.075.579.800.7311.662.4412.763.45Jul. 202020.0015.753.5419.200.6613.175.6916.243.13Aug. 20203.0016.4213.033.800.7714.5711.236.763.65Sep. 202019.0017.111.5918.200.6715.982.5415.243.16Oct. 202015.0017.792.4315.800.6915.750.6518.763.27Nov. 202038.0018.4814.1537.200.5813.6017.6834.242.72Dec. 202030.0019.178.3330.800.6112.4813.4833.762.8930.000.0030.000.00Jan. 202117.0019.872.4516.200.6814.791.8913.243.2115.850.9913.473.01Feb. 20217.0020.5712.687.800.7419.1411.3510.763.5128.1719.7811.023.75Mar. 202115.0021.275.4614.200.6918.132.7211.243.2739.7521.5210.583.84Apr. 202129.0021.985.4429.800.6215.5310.4432.762.9152.3118.0733.723.66May. 202138.0022.7011.0937.200.5820.7312.5134.242.7265.1919.7133.083.56Jun. 202130.0023.415.0730.800.6126.552.6533.762.8977.0736.2135.003.85Jul. 202126.0024.141.4825.200.6328.331.8522.242.9879.1442.1821.023.95Aug. 202125.0024.860.1125.800.6427.141.7128.763.0177.3941.9129.843.87Sep. 202153.0025.5917.9152.200.5225.9617.6749.242.4676.9415.6548.403.01Oct. 202146.0026.3313.4846.800.5524.9714.4049.762.5776.6420.9950.252.91Nov. 202120.0027.065.8919.200.663.5613.7016.243.1382.0251.6816.193.18Dec. 202118.0027.818.3118.800.680.0615.2121.763.1897.3067.2021.282.78Jan. 202248.0028.5513.1447.200.54−40.0459.4944.242.5479.3621.1945.321.81Feb. 202221.0029.316.8621.800.66−113.05110.7824.763.1155.9828.9123.021.67Mar. 202226.0030.063.2225.200.63−177.68161.6522.242.9843.4013.8124.681.05Apr. 202231.0030.820.1431.800.61−91.8493.7734.762.8755.9119.0131.580.45May. 202232.0031.590.3131.200.60−35.4151.0728.242.8563.5923.9332.160.12Jun. 202235.0032.361.9635.800.59−51.9664.4238.762.7859.2917.9934.090.67Jul. 202212.0033.1318.8711.200.71−79.4181.618.243.3653.9737.4813.631.46Aug. 202225.0033.917.1325.800.64−37.1849.7528.763.0159.3627.4956.9925.59Sep. 202229.0034.694.4128.200.62−34.1048.9225.242.9158.8523.1441.709.84MAPE (%)7.110.6427.782.9925.863.82Oct. 202235.0035.480.3641.855.08−81.7586.48−65.9174.7551.9112.5249.5410.77Nov. 202246.0036.276.6610.4024.39−28.1850.81−51.1966.5758.308.4341.153.32MAPE (%)3.5114.7368.6470.6610.487.04Dec. 202237.0735.12−29.08−22.8355.3626.20Jan. 202337.8731.67−150.33−155.2147.9229.32Feb. 202338.6833.40−169.59−168.5045.3513.24Table 8
Prediction results of travel sentiment in Italy.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 202051.0051.000.0051.000.0051.000.0051.000.00Feb. 2020−2.0028.7231.35−1.540.4717.5919.9915.5317.89Mar. 2020−29.0029.8882.93−29.460.6519.7068.59−46.5324.69Apr. 202021.0031.058.3121.460.3821.900.7538.5314.49May. 202037.0032.233.4836.540.3325.118.6819.4712.79Jun. 202047.0033.439.2347.460.3128.2512.7664.5311.92Jul. 202033.0034.631.2332.540.3431.261.3115.4713.18Aug. 202031.0035.853.7031.460.3533.982.2848.5313.38Sep. 202053.0037.0710.4152.540.3036.3410.8935.4711.46Oct. 202045.0038.314.6145.460.3228.9111.1062.5312.09Nov. 202060.0039.5612.7859.540.298.9631.9042.4710.95Dec. 202043.0040.821.5343.460.3221.6414.9460.5312.2643.000.0043.000.00Jan. 202146.0042.092.6845.540.3123.4115.4728.4712.0151.273.6147.320.90Feb. 202153.0043.376.3053.460.3026.5717.2770.5311.4659.564.2952.060.61Mar. 202151.0044.664.2050.540.3011.2626.3233.4711.6167.9411.2251.540.36Apr. 202161.0045.979.3461.460.2821.6724.4378.5310.8977.5510.2860.870.08May. 202154.0047.284.3653.540.3036.3611.4536.4711.3889.0322.7553.710.19Jun. 202162.0048.618.2662.460.2848.418.3979.5310.8298.6922.6562.700.43Jul. 202160.0049.956.2859.540.2948.117.4342.4710.95106.0928.8158.910.68Aug. 202154.0051.311.7554.460.3043.137.0671.5311.38105.3333.3355.460.95Sep. 202163.0052.676.3462.540.2849.728.1545.4710.75107.7227.4361.211.10Oct. 202157.0054.051.8857.460.2955.041.2574.5311.16109.3533.3459.091.33Nov. 202163.0055.444.6462.540.2843.1912.1645.4710.75113.2830.8560.661.44Dec. 202164.0056.844.3764.460.28−38.9362.7681.5310.69121.2934.9366.541.55Jan. 202261.0058.261.7060.540.28−441.13311.8843.4710.89105.1727.4358.321.66Feb. 202252.0059.685.0552.460.30−155.52136.5369.5311.53108.4337.1354.761.81Mar. 202264.0061.121.7563.540.28−180.47149.0646.4710.69102.6423.5661.221.69Apr. 202271.0062.584.9371.460.27−195.12155.6388.5310.25101.1917.6673.731.60May. 202268.0064.042.3567.540.27−103.68102.1950.4710.43106.7823.0965.371.56Jun. 202254.0065.527.4854.460.30−132.48121.0971.5311.38104.6732.9056.471.60Jul. 202246.0067.0214.4045.540.31−344.68267.5928.4712.0195.0233.5843.751.54Aug. 202243.0068.5217.8543.460.32−136.20125.3160.5312.26106.0044.05102.0441.29Sep. 202262.0070.054.9761.540.28−99.5099.6944.4710.82106.3327.3698.8322.74MAPE (%)8.800.3156.1911.7924.103.87Oct. 202259.0071.587.9141.3211.12−181.34151.16−183.40152.45103.1327.7699.1825.27Nov. 202259.0073.138.8913.7928.43−137.71123.72−203.94165.37104.6528.7197.1624.00MAPE (%)8.4019.78137.44158.9128.2424.63Dec. 202274.6965.10−173.70−157.07101.8485.44Jan. 202376.2780.57−382.04−387.68100.1083.42Feb. 202377.8691.89−429.83−393.5598.1862.86Table 9
Prediction results of travel sentiment in Mexico.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 202036.0036.000.0036.000.00Feb. 202049.0023.0217.4446.531.6649.000.0049.000.00Mar. 2020−5.0023.2629.75−2.532.6021.3327.7111.8617.75Apr. 202012.0023.5110.289.532.2121.458.44−3.6213.95May. 202042.0023.7612.8544.471.7420.4315.1956.2210.01Jun. 202027.0024.002.3624.531.9519.346.0314.339.97Jul. 20205.0024.2518.337.472.3518.5112.8715.9910.46Aug. 202031.0024.504.9628.531.8923.106.0321.817.02Sep. 202036.0024.758.2738.471.8224.638.3643.315.37Oct. 202033.0025.006.0230.531.8619.949.8227.664.02Nov. 202042.0025.2511.8044.471.7422.5713.6945.332.34Dec. 202046.0025.5014.0443.531.6910.5524.2844.720.8746.000.0046.000.00Jan. 2021−17.0025.7551.50−14.532.988.1730.33−17.790.95−14.632.85−19.112.54Feb. 2021−5.0026.0032.63−7.472.6049.2457.09−2.162.9927.1833.87−2.602.53Mar. 202112.0026.2512.7314.472.2134.4420.037.134.3547.2431.479.372.35Apr. 202132.0026.514.1629.531.8732.800.6038.855.1956.8218.8034.812.13May. 202135.0026.766.1137.471.8332.821.6126.256.4958.7917.6232.082.16Jun. 202119.0027.016.7316.532.0821.602.1829.578.8858.0232.7921.972.49Jul. 202126.0027.271.0028.471.96−12.6630.6813.729.7555.9023.7323.052.34Aug. 202132.0027.523.3929.531.87−7.8030.1545.8610.5047.0711.4134.862.17Sep. 202133.0027.783.9335.471.8663.6923.0817.7011.5145.089.0930.282.04Oct. 202136.0028.035.8633.531.8263.4120.1552.5912.2054.0213.2538.511.84Nov. 202148.0028.2913.3250.471.6744.342.4730.3011.9634.818.9145.761.51Dec. 202130.0028.541.1227.531.9026.522.6848.6314.3342.749.8031.921.48Jan. 202227.0028.801.4229.471.95−184.69166.687.6315.2528.150.9125.431.23Feb. 202239.0029.067.1536.531.78124.8961.7958.9114.3233.184.1940.170.84Mar. 202236.0029.324.9138.471.82139.3475.9915.7514.8933.351.9535.250.55Apr. 202237.0029.575.4234.531.8051.9510.9157.3814.8730.834.5137.320.23May. 202221.0029.837.3023.472.0446.1620.790.7016.7733.1010.0021.130.10Jun. 202230.0030.090.0727.531.90−33.6748.9850.0115.3923.125.2929.430.44Jul. 202218.0030.3510.4720.472.09−100.55100.47−1.5216.5414.373.0819.000.84Aug. 202220.0030.618.8517.532.06165.51121.2638.8215.6819.400.5018.601.17Sep. 202234.0030.882.3336.471.8496.0646.3216.0713.3823.697.6935.781.33MAPE (%)9.891.9231.469.9411.441.47Oct. 202236.0031.143.5854.6513.7154.4513.5744.996.6137.751.2933.272.01Nov. 202210.0031.4019.455.613.9939.8327.1114.764.3226.4814.99−3.3012.09MAPE (%)11.518.8520.345.478.147.05Dec. 202231.6617.682.2037.9923.04−14.84Jan. 202331.9352.64−18.55−23.5628.186.16Feb. 202332.1932.7234.9232.3928.051.33Table 10
Prediction results of travel sentiment in Spain.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 202043.0043.000.0043.000.00Feb. 202032.0013.2114.2328.052.9932.000.0032.000.00Mar. 2020−32.0014.0867.76−28.055.813.4152.07−10.1532.13Apr. 202014.0014.940.8310.053.475.077.83−6.0717.61May. 20207.0015.828.2410.953.698.251.1725.0916.91Jun. 202016.0016.700.6012.053.4111.373.990.0813.73Jul. 2020−5.0017.5823.77−1.054.1613.5919.578.5914.31Aug. 2020−12.0018.4834.64−15.954.4911.7927.03−23.1212.64Sep. 202028.0019.386.7331.953.097.6615.8936.546.67Oct. 202029.0020.296.7525.053.062.0220.9223.134.55Nov. 202039.0021.2012.8042.952.84−2.4729.8342.142.26Dec. 202037.0022.1210.8633.052.885.6222.9136.630.27Jan. 202124.0023.050.7627.953.19−30.4943.9521.601.9324.000.0024.000.00Feb. 202143.0023.9913.2939.052.76−11.3838.0348.143.5933.356.7538.573.10Mar. 202116.0024.937.7019.953.4113.881.828.176.7543.1323.3920.433.82Apr. 202148.0025.8814.9444.052.673.0830.3558.447.0553.944.0143.572.99May. 202132.0026.843.9135.952.9911.1115.8319.069.8163.5423.8936.433.36Jun. 202133.0027.803.9129.052.9714.6713.7848.3111.5174.3331.0828.573.33Jul. 202123.0028.784.7026.953.21−41.1352.145.4714.2582.5048.3827.433.60Aug. 202133.0029.752.4429.052.97−20.3640.1252.5614.7182.2937.0628.573.33Sep. 202139.0030.745.9442.952.8415.7016.7717.6115.3976.5427.0143.433.19Oct. 202147.0031.7410.3843.052.6924.6915.1770.0015.6574.3618.6142.573.01Nov. 202142.0032.746.5245.952.7812.4820.7917.6217.1779.0226.0746.433.12Dec. 202140.0033.754.4736.052.82−140.81129.1565.5118.2288.8034.8635.573.17Jan. 202232.0034.762.0935.952.99−583.82466.535.6319.98106.1156.1436.433.36Feb. 202242.0035.794.3738.052.78−183.27158.6468.9718.9981.9928.1637.573.12Mar. 202258.0036.8213.4061.952.50−110.35106.5530.7217.2775.9011.3362.432.80Apr. 202235.0037.862.1231.052.93−90.7793.1662.3220.2471.6027.1130.573.28May. 202234.0038.913.6637.952.95−105.71104.266.9220.2170.0526.9038.433.31Jun. 202239.0039.970.7035.052.84−108.12105.8465.5619.1168.2221.0234.573.19Jul. 202213.0041.0324.8116.953.50−134.98130.95−12.7722.8066.8547.6617.433.92Aug. 202221.0042.1017.4417.053.27−47.6356.7245.7120.4261.1333.1616.573.66Sep. 202236.0043.185.2839.952.91−41.1756.7412.6017.2058.9916.9140.433.26MAPE (%)10.313.0959.3313.5426.173.14Oct. 202245.0044.270.5059.119.73−30.0551.76−43.6161.1156.467.9061.6811.50Nov. 202253.0045.374.993.2532.52−63.5576.18−74.7083.4661.355.4638.659.38MAPE (%)2.7421.1263.9772.296.6810.44Dec. 202246.4841.58−46.33−29.4959.2848.91Jan. 202347.5942.72−181.24−192.5357.2430.14Feb. 202348.7144.06−196.35−201.3555.269.50Table 11
Prediction results of travel sentiment in Thailand.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 20209.009.000.009.000.009.000.009.000.00Feb. 2020−2.0028.3130.93−2.490.5018.9621.38−2.670.69Mar. 2020−6.0029.2937.55−5.510.5220.9728.69−5.330.72Apr. 202025.0030.284.2324.510.3923.021.5824.330.54May. 202032.0031.280.5432.490.3725.155.1932.670.51Jun. 202036.0032.292.7335.510.3627.306.4035.330.49Jul. 202047.0033.309.3247.490.3329.4811.9247.670.46Aug. 202043.0034.326.0742.510.3431.717.9042.330.47Sep. 202036.0035.350.4836.490.3633.961.5036.670.49Oct. 202047.0036.397.2246.510.3336.267.3146.330.46Nov. 202050.0037.448.3850.490.3338.607.6050.670.45Dec. 202031.0038.495.7230.510.3740.717.4130.330.51Jan. 202149.0039.556.3449.490.3342.074.6549.670.45Feb. 202146.0040.623.6945.510.3444.870.7845.330.46Mar. 202151.0041.706.1651.490.3247.792.1251.670.4551.000.0051.000.00Apr. 202147.0042.782.8746.510.3345.471.0446.330.4650.442.3444.461.73May. 202153.0043.885.9653.490.3238.199.6853.670.4453.360.2455.541.66Jun. 202157.0044.987.6656.510.3137.8812.1856.330.4356.670.2154.461.62Jul. 202150.0046.092.6150.490.33−4.2436.1650.670.4561.777.8552.541.69Aug. 202143.0047.212.9442.510.34−60.6272.4642.330.4769.5418.5640.461.78Sep. 202155.0048.344.3055.490.32−30.3155.0455.670.4372.2111.1057.541.64Oct. 202145.0049.483.0944.510.34−18.1043.5244.330.4679.4323.7442.461.75Nov. 202152.0050.620.9152.490.320.5133.8752.670.4478.5017.4354.541.67Dec. 202160.0051.775.1459.510.3120.9024.4459.330.4278.5711.6157.461.59Jan. 202250.0052.941.9650.490.33−6.9137.9450.670.4582.5321.6852.541.69Feb. 202260.0054.113.6859.510.31−72.0482.5359.330.4287.8117.3857.461.59Mar. 202243.0055.298.5943.490.34−160.71142.4643.670.4796.1237.1445.541.78Apr. 202266.0056.485.7365.510.30−144.98127.1065.330.4095.9218.0263.461.53May. 202256.0057.681.0856.490.31−30.6655.5556.670.4388.3720.7558.541.63Jun. 202260.0058.890.6959.510.316.5133.4359.330.4285.4215.8957.461.59Jul. 202246.0060.119.6646.490.347.6726.2646.670.4686.1427.4948.541.74Aug. 202251.0061.336.8450.510.3213.0725.1250.330.4585.9423.1448.461.68Sep. 202253.0062.576.2553.490.3222.8519.7153.670.4485.5021.2455.541.66MAPE (%)6.340.3328.880.4615.571.58Oct. 202246.0063.8212.2033.018.8931.3610.039.7324.8484.9226.6678.9422.56Nov. 202259.0065.073.8230.2718.0731.5717.255.2733.7985.3416.5787.5317.94MAPE (%)8.0113.4813.6429.3221.6120.25Dec. 202266.3460.5633.5334.8385.5683.35Jan. 202367.6168.82−56.41−48.8993.7984.56Feb. 202368.8972.12−64.17−56.1494.1365.05Table 12
Prediction results of travel sentiment in Turkey.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 202019.0019.000.0019.000.00Feb. 2020−11.0010.8624.56−9.012.23Mar. 2020−34.0011.1268.37−35.993.01−34.000.00−34.000.00Apr. 202032.0011.3915.6133.991.5114.3613.3734.001.51May. 202025.0011.6610.6823.011.5915.317.7623.001.60Jun. 202011.0011.920.8312.991.7916.314.7813.001.80Jul. 20209.0012.192.937.011.8217.357.667.001.83Aug. 2020−4.0012.4617.14−2.012.0718.2923.22−2.002.08Sep. 202018.0012.734.4716.011.6819.181.0016.001.69Oct. 2020−13.0013.0029.88−11.012.2820.0337.97−11.002.30Nov. 202042.0013.2720.2340.011.4017.4717.2840.001.41Dec. 202014.0013.540.4115.991.74−7.5518.9016.001.75Jan. 202133.0013.8114.4331.011.4914.4913.9231.001.5033.000.0033.000.00Feb. 202114.0014.080.0715.991.7415.521.3316.001.7522.027.0314.550.48Mar. 202137.0014.3516.5335.011.455.5222.9835.001.4638.451.0536.450.40Apr. 202111.0014.633.2712.991.79−21.2329.0313.001.8051.0936.1211.550.49May. 20218.0014.906.396.011.845.851.996.001.8552.1140.857.450.51Jun. 202135.0015.1814.6836.991.4713.3216.0637.001.4863.8621.3835.550.41Jul. 202121.0015.454.5919.011.649.249.7219.001.6566.7837.8320.450.45Aug. 2021−13.0015.7333.02−11.012.28−4.629.63−11.002.3066.7891.70−12.450.63Sep. 202145.0016.0020.0043.011.37−10.8438.5143.001.3860.2810.5444.450.38Oct. 202136.0016.2814.5037.991.46−18.2539.8938.001.4749.459.8936.550.40Nov. 202123.0016.565.2421.011.62−16.1831.8621.001.6242.2515.6522.450.45Dec. 202142.0016.8417.7243.991.40−15.2440.3144.001.4145.762.6542.550.39Jan. 202215.0017.121.8413.011.73−90.2991.5613.001.7451.6231.8414.450.48Feb. 202232.0017.4011.0633.991.51−117.58113.3234.001.5143.808.9432.550.42Mar. 202221.0017.682.7519.011.64−35.3246.5419.001.6526.484.5320.450.45Apr. 202211.0017.966.2712.991.79−3.5813.1313.001.8018.536.7811.550.49May. 20224.0018.2413.692.011.914.480.472.001.9214.8510.443.450.53Jun. 2022−4.0018.5223.46−2.012.074.699.05−2.002.0812.6617.35−3.450.57Jul. 2022−10.0018.8132.01−11.992.21−41.6735.19−12.002.2219.1232.35−10.550.61Aug. 202214.0019.094.4715.991.74−38.2945.8716.001.7514.350.3114.550.48Sep. 202218.0019.371.1716.011.68−7.3121.4516.001.699.397.3017.450.46MAPE (%)13.401.7324.641.6818.790.45Oct. 202232.0019.669.35−0.2124.404.1221.1223.766.246.9518.98−0.5224.63Nov. 202233.0019.959.81−27.1745.248.4218.4816.1212.699.9717.327.9818.81MAPE (%)9.5834.8219.809.4718.1521.72Dec. 202220.2342.839.486.1712.48−27.06Jan. 202320.5231.88−39.70−50.0511.54−33.12Feb. 202320.8121.87−42.67−62.9610.71−17.61Table 13
Prediction results of travel sentiment in UK.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 202015.0015.000.0015.000.0015.000.0015.000.00Feb. 202010.00−0.219.2810.270.24−1.8410.7611.090.99Mar. 2020−28.000.3939.43−28.270.37−1.0037.50−29.091.52Apr. 20206.000.994.736.270.25−0.265.917.091.03May. 2020−1.001.592.62−1.270.270.611.62−2.091.11Jun. 2020−2.002.204.28−1.730.271.533.60−0.911.12Jul. 20203.002.810.192.730.262.420.561.911.06Aug. 202023.003.4215.9223.270.223.2816.0324.090.89Sep. 202026.004.0417.4325.730.213.9217.5224.910.87Oct. 202010.004.664.8610.270.243.296.1011.090.99Nov. 202023.005.2814.4022.730.223.5715.8021.910.89Dec. 2020−18.005.9129.16−17.730.333.0425.66−16.911.33Jan. 2021−18.006.5429.93−18.270.331.2023.42−19.091.33−18.000.00−18.000.00Feb. 2021−14.007.1824.63−13.730.315.8223.05−12.911.27−7.837.17−12.471.78Mar. 20216.007.821.715.730.257.491.414.911.0319.1412.394.471.44Apr. 20217.008.461.377.270.258.871.758.091.0236.1927.288.531.43May. 202112.009.112.5811.730.249.781.9810.910.9849.1333.1610.471.37Jun. 202110.009.760.2210.270.249.120.8011.090.9953.3039.3611.531.39Jul. 202110.0010.410.389.730.244.724.808.910.9951.8538.058.471.39Aug. 202112.0011.070.8312.270.245.725.6013.090.9850.0133.9413.531.37Sep. 202113.0011.741.1212.730.245.286.8311.910.9746.0529.2511.471.35Oct. 202122.0012.407.8722.270.223.5115.1523.090.9051.8424.4623.531.25Nov. 202128.0013.0711.6627.730.214.1318.6526.910.8553.6720.0526.471.20Dec. 202113.0013.750.6613.270.24−9.7520.1314.090.9763.3844.5914.531.35Jan. 202224.0014.437.7223.730.22−26.8841.0422.910.8848.7019.9222.471.23Feb. 202217.0015.111.6217.270.23−1.9316.1818.090.9433.0913.7618.531.31Mar. 202217.0015.791.0316.730.23−9.4622.6115.910.9433.5614.1515.471.31Apr. 202224.0016.496.0624.270.224.3115.8825.090.8829.324.2925.531.23May. 202235.0017.1813.2034.730.2011.5717.3533.910.8122.849.0133.471.13Jun. 202221.0017.882.5821.270.2210.508.6722.090.9019.661.1022.531.26Jul. 2022−6.0018.5826.15−6.270.289.1416.11−7.091.1618.0925.63−7.531.63Aug. 20223.0019.2915.823.270.2615.2611.904.091.0613.7410.434.531.49Sep. 202219.0020.000.8418.730.2317.960.8717.910.9212.075.8317.471.29MAPE (%)9.100.2412.580.9919.711.30Oct. 202225.0020.723.4331.194.9513.928.8726.851.4816.696.6512.0510.36Nov. 202227.0021.444.38−7.2226.9418.486.71−9.6128.8315.459.100.7820.65MAPE (%)3.9015.957.7915.157.8715.50Dec. 202222.1627.4418.9126.2614.37−13.28Jan. 202322.8920.037.174.4713.44−25.23Feb. 202323.6219.707.004.5712.62−29.14Table 14
Prediction results of travel sentiment in the US.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 20209.009.000.009.000.009.000.009.000.00Feb. 202014.009.094.3013.100.79−0.7612.9531.6915.52Mar. 2020−25.009.7646.35−24.101.202.2536.33−42.6923.59Apr. 2020−2.0010.4412.69−2.900.923.115.2215.6918.05May. 20205.0011.115.825.900.865.500.48−12.6916.85Jun. 2020−1.0011.7912.92−1.900.916.737.8016.6917.87Jul. 20205.0012.487.125.900.861.373.46−12.6916.85Aug. 202010.0013.172.889.100.823.715.7227.6916.08Sep. 202023.0013.867.4323.900.736.5413.385.3114.38Oct. 202023.0014.566.8622.100.73−0.5319.1340.6914.38Nov. 202035.0015.2614.6235.900.67−33.0150.3817.3113.10Dec. 202033.0015.9612.8132.100.68−70.0477.4750.6913.3033.000.0033.000.00Jan. 2021−1.0016.6817.85−0.100.91−79.5179.30−18.6917.8713.7714.921.042.06Feb. 202134.0017.3912.4033.100.67−32.5449.6651.6913.2033.010.7432.341.24Mar. 202128.0018.117.7328.900.70−25.8142.0410.3113.8252.1918.9029.250.97Apr. 202125.0018.834.9324.100.72−29.6943.7542.6914.1566.2032.9624.200.64May. 202127.0019.565.8627.900.71−11.4530.289.3113.9369.1333.1727.340.27Jun. 202127.0020.295.2826.100.711.2620.2744.6913.9369.3533.3527.130.10Jul. 202119.0021.031.7119.900.75−20.0432.811.3114.8668.8141.8618.410.50Aug. 20219.0021.7711.728.100.82−102.27102.0826.6916.2368.7654.8210.050.96Sep. 202123.0022.520.3923.900.73−111.26109.155.3114.3870.2338.4021.531.20Oct. 202140.0023.2711.9539.100.64−73.4081.0057.6912.6468.2220.1641.871.34Nov. 202152.0024.0218.4152.900.59−81.8588.0634.3111.6472.8413.7149.771.46Dec. 202129.0024.783.2728.100.70−223.65195.8646.6913.7168.7630.8231.531.96Jan. 202223.0025.552.0723.900.73−783.78655.925.3114.3846.2118.8720.222.26Feb. 202227.0026.320.5426.100.71−213.76189.5744.6913.9355.6822.5929.972.34Mar. 202230.0027.092.2430.900.69−107.37105.6712.3113.6155.0319.2626.912.37Apr. 202229.0027.870.8828.100.70−120.73116.0746.6913.7154.7919.9932.142.43May. 202233.0028.653.2733.900.68−203.80178.0515.3113.3049.6912.5529.882.34Jun. 202225.0029.443.5524.100.72−243.02214.4242.6914.1545.9016.7228.032.42Jul. 20224.0030.2325.224.900.86−278.33271.47−13.6917.0143.4237.901.132.76Aug. 20228.0031.0321.327.100.83−250.91239.7325.6916.3842.0231.5029.2919.71Sep. 202232.0031.830.1332.900.68−208.99182.5714.3113.4043.798.9343.128.42MAPE (%)8.930.7498.7914.5523.732.63Oct. 202229.0032.642.8236.655.93−176.71159.46−144.26134.3144.9812.3932.252.52Nov. 202244.0033.457.32−0.4130.84−196.83167.25−241.77198.4540.722.2840.042.75MAPE (%)5.0718.39163.35166.387.342.64Dec. 202234.2720.94−247.15−234.5836.4513.51Jan. 202335.0929.88−396.86−415.0434.04−7.96Feb. 202335.9222.23−429.32−419.3532.57−9.22Several common grounds can be summarized from the prediction results from the top 10 destinations. First of all, the majority of the grey prediction models can fit in the real data well, despite the fact that data lengths vary from one country to another. This shows how flexible the grey prediction models are to changing data lengths and conditions in various countries. Second, on the one hand, the grey prediction model with incorporated COVID-19 and vaccinations might better reflect the real scenario. On the other hand, the hybrid prediction models, F-GM (1, 1) and F-GM (1,N), are more accurate than the original models in both of the model fitting and ex-post testing, nevertheless. There are, however, certain exceptions. The predictions for Italy and Mexico in particular showed extremely substantial fluctuations in the model fitting that simply accounted for the COVID-19 shock effect, despite the residual modification being applied. Finally, the development trend of travel sentiment had been deflected and even presented the opposite development trajectories by introducing different shock effects. Specifically, the pandemic exerted huge downward pressure on travel sentiment by only considering the shock effect of COVID-19 in Phase II. On the contrary, travel sentiment in most countries showed an increasing trend rather than a downward trend by considering the effects of COVID-19 and vaccination simultaneously in Phase III. Therefore, vaccine adoption plays an important role in fighting against COVID-19, and it contributes to tourism recovery.


## 4.1. Comparative Analysis of the Shock Effects of COVID-19 and Vaccination

The development tendency and prediction accuracy of the system will be significantly influenced by past performance, development features, and the relative influencing factors. In order to examine the shock effects of COVID-19 and vaccination as relevant factors, this paper used the original GM (1, 1) and GM (1,N) models as well as the proposed F-GM (1, 1) and F-GM (1, N) models provided in Section 3 to forecast travel sentiment globally and in the top 10 destinations. The entire procedure can be broken down into three phases: the no-epidemic phase, the phase of COVID-19 outbreaks, and the phase of COVID-19 vaccination coexistence. In Phase I, without pandemic shock, the previous developing trend in travel sentiment will persist. Therefore, the GM (1, 1) and F-GM (1, 1) models were used to predict travel sentiment by simply accounting for the temporal effects.If a shock is introduced into a system at a specific time, the impact will cause the initial trend to shift. The global alarm over the pandemic, which had a significant impact on travel sentiment, was exacerbated by the rise in the overall cases of COVID-19. Tourists’ strong disapproval of tourism growth may further depress travel sentiment. In order to forecast travel sentiment, COVID-19 was added as a relevant variable to the GM (1,N) model and F-GM (1, N) model in Phase II.To further assess and forecast travel sentiment, the shock effects of the COVID-19 and vaccination are considered simultaneously in Phase III. In several countries, the pandemic was successfully controlled once COVID-19 vaccines were developed, produced, and administered. Citizens’ confidence in tourism would return as a result, potentially increasing travel sentiment. On the premise of maintaining the relevant variable of the COVID-19 as constant, the paper introduced the vaccination as a relevant variable in the GM (1,N) and the F-GM (1, N) model to predict travel sentiment in Phase III.


## 4.2. Data Collection

The duration of the data differs among the top 10 destinations, due to the varying timing of COVID-19 confirmation and the lengthy procedure involved in vaccine research, development, and administration. Travel sentiment was represented using the monthly net sentiment scores from the UNWTO Tourism Recovery Tracker. COVID-19 and vaccine data, which were represented by the monthly COVID-19 cases per million and monthly vaccinations per hundred, respectively, were derived from Our World in Data. Data from each country’s beginning month through September 2022 were reserved for model fitting, and the data from October to November 2022 were reserved for ex-post testing. Table1 displays the data lengths for various countries.Table 1
The length of the data.
NationsTravel sentimentsCOVID-19 casesVaccinationsWorld, China, Germany, Italy, USJan. 2020–Nov. 2022Jan. 2020–Nov. 2022Dec. 2020–Nov. 2022France, UKJan. 2020–Nov. 2022Jan. 2020–Nov. 2022Jan. 2020–Nov. 2022MexicoJan. 2020–Nov. 2022Feb. 2020–Nov. 2022Dec. 2020–Nov. 2022SpainJan. 2020–Nov. 2022Feb. 2020–Nov. 2022Jan. 2020–Nov. 2022ThailandJan. 2020–Nov. 2022Jan. 2020–Nov. 2022Mar. 2020–Nov. 2022TurkeyJan. 2020–Nov. 2022Mar. 2020–Nov. 2022Jan. 2020–Nov. 2022


## 4.3. Predictive Analysis of Travel Sentiment

Because of the large number of countries and the similar analysis process, this paper used global travel sentiment prediction as an example to analyze the shock effects of COVID-19 and vaccination by following the computation steps in Section3. The prediction results of global travel sentiment are shown in Table 2. In more detail, the MAPE of the GM (1, 1), F-GM (1, 1), GM (1, N), and F-GM (1, N) models for model fitting in Phase I, II, and III is 3.53%, 0.86%, 21.14%, 1.48%, 23.86%, and 1.56%, respectively. The MAPE is 2.68%, 8.14%, 25.16%, 24.88%, 11.57%, and 6.52%, respectively, for ex-post testing. When shock effects are not introduced in Phase I, the MAPE of the F-GM (1, 1) model is better for model fitting than the GM (1, 1) model, but the F-GM (1, 1) model is worse for ex-post testing. The F-GM (1, N) model, which combined the residual modification model, outperformed the GM (1, 1) model in the Phase II and III, both in terms of model fitting and ex-post testing. Beyond all doubt, the grey prediction model integrated with modification model would improve the prediction accuracy.Table 2
Forecasting results of the competing models for global travel sentiment.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 202033.0033.000.0033.000.0033.000.0033.000.00Feb. 202030.0024.484.2428.820.9119.148.3532.021.55Mar. 202010.0024.9913.6311.181.0720.569.607.981.84Apr. 202019.0025.515.4717.820.9921.722.2921.021.70May. 202024.0026.021.6325.180.9522.880.9021.981.63Jun. 202025.0026.541.2323.820.9423.711.0327.021.62Jul. 202025.0027.061.6426.180.9423.820.9422.981.62Aug. 202027.0027.580.4525.820.9324.242.1729.021.59Sep. 202034.0028.104.4035.180.8824.646.9931.981.51Oct. 202031.0028.621.8129.820.9023.335.8533.021.54Nov. 202038.0029.156.4139.180.8520.4612.7135.981.46Dec. 202040.0029.687.3738.820.8417.9415.7642.021.4440.000.0040.000.00Jan. 202123.0030.215.8624.180.9617.584.4020.981.6424.231.0022.190.66Feb. 202128.0030.742.1426.820.9223.153.7930.021.5840.9410.1128.800.63Mar. 202128.0031.282.5629.180.9220.395.9425.981.5854.3720.6027.220.61Apr. 202131.0031.820.6229.820.9013.0613.6933.021.5464.4825.5631.740.56May. 202132.0032.360.2733.180.8914.8413.0029.981.5374.2332.0031.320.52Jun. 202134.0032.900.8232.820.8822.108.8836.021.5184.3637.5834.610.45Jul. 202131.0033.441.8732.180.9017.5410.2728.981.5487.2842.9630.480.40Aug. 202130.0033.993.0728.820.9112.0813.7932.021.5590.6246.6330.420.32Sep. 202135.0034.540.3436.180.8715.7714.2532.981.5089.7240.5334.690.23Oct. 202144.0035.096.1942.820.8219.1017.2946.021.4088.7931.1044.200.14Nov. 202145.0035.646.4546.180.8115.3420.4542.981.3989.5330.7144.920.06Dec. 202150.0036.209.2048.820.790.0833.2852.021.3588.5225.6849.960.03Jan. 202237.0036.760.1838.180.86−101.97101.4434.981.4768.6723.1237.160.12Feb. 202239.0037.321.2137.820.85−61.7272.4641.021.4570.8322.9038.720.20Mar. 202241.0037.882.2142.180.84−57.7670.0438.981.4367.0818.5041.390.27Apr. 202241.0038.441.8139.820.84−17.1141.2143.021.4368.0819.2140.510.35May. 202241.0039.011.4142.180.84−3.0031.2038.981.4366.6918.2241.580.41Jun. 202240.0039.580.3038.820.84−7.1233.6642.021.4464.4017.4339.340.47Jul. 202229.0040.158.6530.180.91−32.1647.4126.981.5759.1023.3329.720.56Aug. 202229.0040.739.0927.820.91−27.2143.5731.021.5757.6622.2255.6320.64Sep. 202236.0041.303.9037.180.87−6.0430.9133.981.4857.2215.6145.096.68MAPE (%)3.530.8621.141.4823.861.56Oct. 202236.0041.884.3346.227.518.6320.1321.5010.6655.6114.4253.5712.92Nov. 202241.0042.461.0428.658.76−1.5630.19−14.1439.1153.308.7341.170.12MAPE (%)2.688.1425.1624.8811.576.52To further forecast global travel sentiment, the GM (1, 1) model is used to predict the relevant variables from December 2022 through February 2023. The results are displayed in Table3, showing that the total cases per million of COVID-19 remained on the rise in 2022 and 2023 while many countries adopted strict prevention and quarantine measures and even the complete border closures. In addition, it is worth noting that most people believe that vaccines are one of the best methods against the COVID-19. The future vaccination concentration rate has decreased slightly but is otherwise basically identical.Table 3
Prediction of relevant variables.
DatesCOVID-19VaccinationsDec. 20222148.324.90Jan. 20233252.114.76Feb. 20233272.484.62The predicted values of COVID-19 and vaccination are substituted into the GM models with a residual modification model to further forecast global travel sentiment. Table4 shows the forecasting of global travel sentiment for the different phases. Also, the actual values and predicted values obtained by the different models are intuitively displayed in Figure 1. It is very obvious from Figure 1 that the prediction of travel sentiment varies among the different models. More specifically, under the influence of previous travel sentiment, Phase I, although the travel sentiment fluctuated, it remained stable, with a small decline in February 2023. After introducing the shock effects of COVID-19 (Phase II), on the one hand, the model can fit the actual value well. However, on the other hand, the out-of-sample prediction of travel sentiment showed a downward trend. This can be interpreted as showing that the negative sentiment of global tourists is still high, that they believe that tourism is still seriously affected by the pandemic, and that they are not confident in tourism recovery. The shock effects of the pandemic and the vaccine are included in Phase III. The extrapolated findings show that travel sentiment has gradually declined along with the drop in the vaccination proportion. However, the travel sentiment is still positive, showing that tourists are growing more confident in the tourism. To a certain extent, the prediction results prove the effectiveness of pandemic measures and the correctness of vaccination.Table 4
Predicted travel sentiment in different countries.
DatesPhase IPhase IIPhase IIIDec. 202235.36−14.2724.12Jan. 202342.79−51.6618.26Feb. 202341.51−53.676.44Figure 1
Global travel sentiment predictions from Jan. 2020 to Jun. 2022.Phase III includes the vaccines and the pandemic’s shock effects.For details of the actual values and predicted values of travel sentiment for the top 10 destinations, refer to Tables5–14. Except for Thailand (see Table 11), which has consistently maintained a high level of travel sentiment, China (see Table 5) and Turkey (see Table 12) have experienced significant fluctuations among the three Asian nations. Future trends show an upward tendency for Turkey but a declining trend for Thailand and China. In contrast to the Asian nations, the sample data indicate that the five European countries of France (see Table 6), Germany (see Table 7), Italy (see Table 8), Spain (see Table 10), and the UK (see Table 13) have a rather positive overall travel sentiment. Due to the unpredictability and frequent outbreaks of the COVID-19, travel sentiment will similarly move negatively in the upcoming months as it does in Asian countries. The US (see Table 14) and Mexico (see Table 9), two countries in the Americas, both experienced a through in traveler sentiment in January 2021 before slowly rebounding.Table 5
Prediction results of travel sentiment in China.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 2020−56.00−56.000.00−56.000.00−56.000.00−56.000.00Feb. 2020−66.00−40.4775.10−66.100.30−39.7277.29−66.692.02Mar. 2020−74.00−38.92134.91−73.900.39−38.53136.43−73.312.64Apr. 2020−79.00−37.34198.37−79.100.48−37.30198.57−79.693.27May. 2020−57.00−35.7249.49−56.900.23−36.0348.76−56.311.60Jun. 2020−44.00−34.0517.76−44.100.18−34.7416.53−44.691.23Jul. 2020−52.00−32.3540.95−51.900.21−33.4338.69−51.311.43Aug. 2020−36.00−30.598.45−36.100.16−32.096.11−36.691.07Sep. 2020−56.00−28.7961.83−55.900.23−30.7157.48−55.311.56Oct. 2020−50.00−26.9546.10−50.100.20−29.3141.38−50.691.37Nov. 2020−5.00−25.0621.11−4.900.11−27.8724.07−4.310.72Dec. 2020−20.00−23.123.89−20.100.13−26.397.99−20.690.86−20.000.00−20.000.00Jan. 2021−24.00−21.123.78−23.900.13−24.971.28−23.310.90−8.0221.02−26.583.39Feb. 2021−10.00−19.0810.09−10.100.11−23.3614.85−10.690.767.3719.30−8.341.84Mar. 20210.00−16.9816.980.100.10−21.7921.790.690.6920.0520.05−0.700.70Apr. 202119.00−14.8328.4318.900.08−20.2032.9418.310.5832.1311.0318.730.23May. 202115.00−12.6324.0215.100.09−18.5629.1915.690.6051.6931.9016.231.07Jun. 202122.00−10.3626.5321.900.08−16.9031.8921.310.5669.9439.3019.831.78Jul. 202117.00−8.0421.4017.100.09−15.2227.5417.690.5966.8542.6120.062.61Aug. 2021−7.00−5.661.44−7.100.11−13.527.01−7.690.7470.7683.62−10.884.17Sep. 202124.00−3.2221.9524.100.08−11.7028.7924.690.5554.4524.5628.613.72Oct. 202138.00−0.7128.0537.900.07−9.8834.7037.310.5047.857.1432.763.80Nov. 202112.001.869.0512.100.09−8.0617.9112.690.6158.8441.8217.765.14Dec. 202119.004.5012.1818.900.08−6.2921.2518.310.5864.6238.3412.865.16Jan. 202225.007.2114.2325.100.08−4.4323.5425.690.5550.5520.4431.395.11Feb. 202233.009.9917.3032.900.08−2.4626.6632.310.5245.749.5826.514.88Mar. 20221.0012.8411.721.100.10−7.638.551.690.6828.7627.497.456.39Apr. 20223.0015.7612.392.900.10−43.2044.852.310.67−57.7959.02−3.276.09May. 20228.0018.769.968.100.09−4.6611.728.690.6418.8410.0413.955.51Jun. 202217.0021.844.1316.900.092.5712.3316.310.5926.678.2711.514.69Jul. 2022−2.0024.9927.54−1.900.103.515.63−1.310.7022.7225.222.915.01Aug. 2022−26.0028.2373.28−26.100.142.3938.37−26.690.9314.2954.44−30.225.70Sep. 202215.0031.5514.3915.100.095.678.1115.690.6014.840.1318.442.99MAPE (%)31.720.1433.400.9527.063.64Oct. 202218.0034.9614.379.337.356.879.43−20.1032.2912.035.06−6.5220.78Nov. 202215.0038.4620.403.4810.02−3.4216.02−38.2046.265.768.04−9.9521.70MAPE (%)17.398.6812.7339.286.5521.24Dec. 202242.040.28−4.07−46.462.63−18.13Jan. 202345.7224.54−5.06−25.34−0.49−13.88Feb. 202349.5039.45−6.42−16.36−3.59−39.05Table 6
Prediction results of travel sentiment in France.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 202032.0032.000.0032.000.0032.000.0032.000.00Feb. 202024.0025.050.8422.151.4923.630.3023.120.71Mar. 2020−9.0025.5337.95−7.152.0324.3136.60−8.120.96Apr. 202034.0026.025.9632.151.3824.956.7633.120.65May. 202025.0026.501.2026.851.4825.680.5425.880.70Jun. 202037.0026.997.3035.151.3526.397.7536.120.64Jul. 202040.0027.498.9441.851.3227.089.2340.880.63Aug. 202019.0027.987.5517.151.5527.697.3018.120.74Sep. 202025.0028.472.7826.851.4828.052.4425.880.70Oct. 202017.0028.9710.2315.151.5827.709.1416.120.75Nov. 202045.0029.4710.7146.851.2827.9811.7445.880.60Dec. 202028.0029.971.5426.151.4529.381.0827.120.68Jan. 202135.0030.483.3536.851.3729.504.0735.880.6535.000.0035.000.00Feb. 202141.0030.987.1139.151.3130.047.7740.120.6240.152.0636.2711.55Mar. 202140.0031.496.0841.851.3229.577.4540.880.6340.250.6344.7311.83Apr. 202135.0032.002.2333.151.3729.673.9534.120.6541.6719.0730.2713.53May. 202139.0032.514.6740.851.3333.094.2539.880.6340.032.6543.7312.14Jun. 202143.0033.026.9841.151.2933.616.5742.120.6141.224.1438.2711.01Jul. 202115.0033.5316.1216.851.6133.3915.9915.880.7643.56190.4019.7331.56Aug. 202132.0034.051.5530.151.4032.900.6831.120.6642.3232.2427.2714.79Sep. 202118.0034.5714.0419.851.5734.9114.3318.880.7434.8593.6022.7326.30Oct. 202152.0035.0911.1250.151.2236.0510.4951.120.5830.5741.2147.279.10Nov. 202137.0035.611.0138.851.3535.081.4037.880.6433.688.9841.7312.79Dec. 202126.0036.148.0524.151.4726.810.6425.120.7057.73122.0221.2718.21Jan. 202233.0036.672.7634.851.39−8.9631.5533.880.66119.03260.6937.7314.35Feb. 202236.0037.200.8834.151.3617.8713.3335.120.6463.0375.0831.2713.15Mar. 202256.0037.7311.7157.851.1920.6322.6856.880.5654.293.0660.738.45Apr. 202252.0038.269.0450.151.2219.3521.4851.120.5855.546.8047.279.10May. 202257.0038.7911.6058.851.1831.8316.0357.880.5632.2643.4061.738.31Jun. 202250.0039.337.1148.151.2327.7814.8149.120.5838.9122.1845.279.47Jul. 202210.0039.8727.1611.851.6820.389.4410.880.8051.86418.5714.7347.34Aug. 202225.0040.4112.3323.151.4834.567.6424.120.7024.153.4120.2718.94Sep. 202234.0040.965.1935.851.3832.870.8434.880.6527.1620.1338.7313.92MAPE (%)8.031.379.340.6565.2515.04Oct. 202239.0041.501.8038.600.2829.187.0628.687.4342.057.8238.162.15Nov. 202240.0042.051.469.3721.8832.365.46−0.0728.6241.854.6246.3315.83MAPE (%)1.6311.086.2618.026.228.99Dec. 202242.6048.7329.4737.6541.7030.29Jan. 202343.1543.5019.3219.5241.6145.31Feb. 202343.7151.8617.8027.5441.5838.63Table 7
Prediction results of travel sentiment in Germany.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 202022.0022.000.0022.000.0022.000.0022.000.00Feb. 202018.0012.424.7318.800.685.9110.2421.763.18Mar. 2020−12.0013.0828.50−12.800.917.2621.88−15.764.27Apr. 202011.0013.742.4711.800.728.512.2414.763.39May. 20209.0014.414.968.200.7310.131.035.243.45Jun. 20209.0015.075.579.800.7311.662.4412.763.45Jul. 202020.0015.753.5419.200.6613.175.6916.243.13Aug. 20203.0016.4213.033.800.7714.5711.236.763.65Sep. 202019.0017.111.5918.200.6715.982.5415.243.16Oct. 202015.0017.792.4315.800.6915.750.6518.763.27Nov. 202038.0018.4814.1537.200.5813.6017.6834.242.72Dec. 202030.0019.178.3330.800.6112.4813.4833.762.8930.000.0030.000.00Jan. 202117.0019.872.4516.200.6814.791.8913.243.2115.850.9913.473.01Feb. 20217.0020.5712.687.800.7419.1411.3510.763.5128.1719.7811.023.75Mar. 202115.0021.275.4614.200.6918.132.7211.243.2739.7521.5210.583.84Apr. 202129.0021.985.4429.800.6215.5310.4432.762.9152.3118.0733.723.66May. 202138.0022.7011.0937.200.5820.7312.5134.242.7265.1919.7133.083.56Jun. 202130.0023.415.0730.800.6126.552.6533.762.8977.0736.2135.003.85Jul. 202126.0024.141.4825.200.6328.331.8522.242.9879.1442.1821.023.95Aug. 202125.0024.860.1125.800.6427.141.7128.763.0177.3941.9129.843.87Sep. 202153.0025.5917.9152.200.5225.9617.6749.242.4676.9415.6548.403.01Oct. 202146.0026.3313.4846.800.5524.9714.4049.762.5776.6420.9950.252.91Nov. 202120.0027.065.8919.200.663.5613.7016.243.1382.0251.6816.193.18Dec. 202118.0027.818.3118.800.680.0615.2121.763.1897.3067.2021.282.78Jan. 202248.0028.5513.1447.200.54−40.0459.4944.242.5479.3621.1945.321.81Feb. 202221.0029.316.8621.800.66−113.05110.7824.763.1155.9828.9123.021.67Mar. 202226.0030.063.2225.200.63−177.68161.6522.242.9843.4013.8124.681.05Apr. 202231.0030.820.1431.800.61−91.8493.7734.762.8755.9119.0131.580.45May. 202232.0031.590.3131.200.60−35.4151.0728.242.8563.5923.9332.160.12Jun. 202235.0032.361.9635.800.59−51.9664.4238.762.7859.2917.9934.090.67Jul. 202212.0033.1318.8711.200.71−79.4181.618.243.3653.9737.4813.631.46Aug. 202225.0033.917.1325.800.64−37.1849.7528.763.0159.3627.4956.9925.59Sep. 202229.0034.694.4128.200.62−34.1048.9225.242.9158.8523.1441.709.84MAPE (%)7.110.6427.782.9925.863.82Oct. 202235.0035.480.3641.855.08−81.7586.48−65.9174.7551.9112.5249.5410.77Nov. 202246.0036.276.6610.4024.39−28.1850.81−51.1966.5758.308.4341.153.32MAPE (%)3.5114.7368.6470.6610.487.04Dec. 202237.0735.12−29.08−22.8355.3626.20Jan. 202337.8731.67−150.33−155.2147.9229.32Feb. 202338.6833.40−169.59−168.5045.3513.24Table 8
Prediction results of travel sentiment in Italy.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 202051.0051.000.0051.000.0051.000.0051.000.00Feb. 2020−2.0028.7231.35−1.540.4717.5919.9915.5317.89Mar. 2020−29.0029.8882.93−29.460.6519.7068.59−46.5324.69Apr. 202021.0031.058.3121.460.3821.900.7538.5314.49May. 202037.0032.233.4836.540.3325.118.6819.4712.79Jun. 202047.0033.439.2347.460.3128.2512.7664.5311.92Jul. 202033.0034.631.2332.540.3431.261.3115.4713.18Aug. 202031.0035.853.7031.460.3533.982.2848.5313.38Sep. 202053.0037.0710.4152.540.3036.3410.8935.4711.46Oct. 202045.0038.314.6145.460.3228.9111.1062.5312.09Nov. 202060.0039.5612.7859.540.298.9631.9042.4710.95Dec. 202043.0040.821.5343.460.3221.6414.9460.5312.2643.000.0043.000.00Jan. 202146.0042.092.6845.540.3123.4115.4728.4712.0151.273.6147.320.90Feb. 202153.0043.376.3053.460.3026.5717.2770.5311.4659.564.2952.060.61Mar. 202151.0044.664.2050.540.3011.2626.3233.4711.6167.9411.2251.540.36Apr. 202161.0045.979.3461.460.2821.6724.4378.5310.8977.5510.2860.870.08May. 202154.0047.284.3653.540.3036.3611.4536.4711.3889.0322.7553.710.19Jun. 202162.0048.618.2662.460.2848.418.3979.5310.8298.6922.6562.700.43Jul. 202160.0049.956.2859.540.2948.117.4342.4710.95106.0928.8158.910.68Aug. 202154.0051.311.7554.460.3043.137.0671.5311.38105.3333.3355.460.95Sep. 202163.0052.676.3462.540.2849.728.1545.4710.75107.7227.4361.211.10Oct. 202157.0054.051.8857.460.2955.041.2574.5311.16109.3533.3459.091.33Nov. 202163.0055.444.6462.540.2843.1912.1645.4710.75113.2830.8560.661.44Dec. 202164.0056.844.3764.460.28−38.9362.7681.5310.69121.2934.9366.541.55Jan. 202261.0058.261.7060.540.28−441.13311.8843.4710.89105.1727.4358.321.66Feb. 202252.0059.685.0552.460.30−155.52136.5369.5311.53108.4337.1354.761.81Mar. 202264.0061.121.7563.540.28−180.47149.0646.4710.69102.6423.5661.221.69Apr. 202271.0062.584.9371.460.27−195.12155.6388.5310.25101.1917.6673.731.60May. 202268.0064.042.3567.540.27−103.68102.1950.4710.43106.7823.0965.371.56Jun. 202254.0065.527.4854.460.30−132.48121.0971.5311.38104.6732.9056.471.60Jul. 202246.0067.0214.4045.540.31−344.68267.5928.4712.0195.0233.5843.751.54Aug. 202243.0068.5217.8543.460.32−136.20125.3160.5312.26106.0044.05102.0441.29Sep. 202262.0070.054.9761.540.28−99.5099.6944.4710.82106.3327.3698.8322.74MAPE (%)8.800.3156.1911.7924.103.87Oct. 202259.0071.587.9141.3211.12−181.34151.16−183.40152.45103.1327.7699.1825.27Nov. 202259.0073.138.8913.7928.43−137.71123.72−203.94165.37104.6528.7197.1624.00MAPE (%)8.4019.78137.44158.9128.2424.63Dec. 202274.6965.10−173.70−157.07101.8485.44Jan. 202376.2780.57−382.04−387.68100.1083.42Feb. 202377.8691.89−429.83−393.5598.1862.86Table 9
Prediction results of travel sentiment in Mexico.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 202036.0036.000.0036.000.00Feb. 202049.0023.0217.4446.531.6649.000.0049.000.00Mar. 2020−5.0023.2629.75−2.532.6021.3327.7111.8617.75Apr. 202012.0023.5110.289.532.2121.458.44−3.6213.95May. 202042.0023.7612.8544.471.7420.4315.1956.2210.01Jun. 202027.0024.002.3624.531.9519.346.0314.339.97Jul. 20205.0024.2518.337.472.3518.5112.8715.9910.46Aug. 202031.0024.504.9628.531.8923.106.0321.817.02Sep. 202036.0024.758.2738.471.8224.638.3643.315.37Oct. 202033.0025.006.0230.531.8619.949.8227.664.02Nov. 202042.0025.2511.8044.471.7422.5713.6945.332.34Dec. 202046.0025.5014.0443.531.6910.5524.2844.720.8746.000.0046.000.00Jan. 2021−17.0025.7551.50−14.532.988.1730.33−17.790.95−14.632.85−19.112.54Feb. 2021−5.0026.0032.63−7.472.6049.2457.09−2.162.9927.1833.87−2.602.53Mar. 202112.0026.2512.7314.472.2134.4420.037.134.3547.2431.479.372.35Apr. 202132.0026.514.1629.531.8732.800.6038.855.1956.8218.8034.812.13May. 202135.0026.766.1137.471.8332.821.6126.256.4958.7917.6232.082.16Jun. 202119.0027.016.7316.532.0821.602.1829.578.8858.0232.7921.972.49Jul. 202126.0027.271.0028.471.96−12.6630.6813.729.7555.9023.7323.052.34Aug. 202132.0027.523.3929.531.87−7.8030.1545.8610.5047.0711.4134.862.17Sep. 202133.0027.783.9335.471.8663.6923.0817.7011.5145.089.0930.282.04Oct. 202136.0028.035.8633.531.8263.4120.1552.5912.2054.0213.2538.511.84Nov. 202148.0028.2913.3250.471.6744.342.4730.3011.9634.818.9145.761.51Dec. 202130.0028.541.1227.531.9026.522.6848.6314.3342.749.8031.921.48Jan. 202227.0028.801.4229.471.95−184.69166.687.6315.2528.150.9125.431.23Feb. 202239.0029.067.1536.531.78124.8961.7958.9114.3233.184.1940.170.84Mar. 202236.0029.324.9138.471.82139.3475.9915.7514.8933.351.9535.250.55Apr. 202237.0029.575.4234.531.8051.9510.9157.3814.8730.834.5137.320.23May. 202221.0029.837.3023.472.0446.1620.790.7016.7733.1010.0021.130.10Jun. 202230.0030.090.0727.531.90−33.6748.9850.0115.3923.125.2929.430.44Jul. 202218.0030.3510.4720.472.09−100.55100.47−1.5216.5414.373.0819.000.84Aug. 202220.0030.618.8517.532.06165.51121.2638.8215.6819.400.5018.601.17Sep. 202234.0030.882.3336.471.8496.0646.3216.0713.3823.697.6935.781.33MAPE (%)9.891.9231.469.9411.441.47Oct. 202236.0031.143.5854.6513.7154.4513.5744.996.6137.751.2933.272.01Nov. 202210.0031.4019.455.613.9939.8327.1114.764.3226.4814.99−3.3012.09MAPE (%)11.518.8520.345.478.147.05Dec. 202231.6617.682.2037.9923.04−14.84Jan. 202331.9352.64−18.55−23.5628.186.16Feb. 202332.1932.7234.9232.3928.051.33Table 10
Prediction results of travel sentiment in Spain.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 202043.0043.000.0043.000.00Feb. 202032.0013.2114.2328.052.9932.000.0032.000.00Mar. 2020−32.0014.0867.76−28.055.813.4152.07−10.1532.13Apr. 202014.0014.940.8310.053.475.077.83−6.0717.61May. 20207.0015.828.2410.953.698.251.1725.0916.91Jun. 202016.0016.700.6012.053.4111.373.990.0813.73Jul. 2020−5.0017.5823.77−1.054.1613.5919.578.5914.31Aug. 2020−12.0018.4834.64−15.954.4911.7927.03−23.1212.64Sep. 202028.0019.386.7331.953.097.6615.8936.546.67Oct. 202029.0020.296.7525.053.062.0220.9223.134.55Nov. 202039.0021.2012.8042.952.84−2.4729.8342.142.26Dec. 202037.0022.1210.8633.052.885.6222.9136.630.27Jan. 202124.0023.050.7627.953.19−30.4943.9521.601.9324.000.0024.000.00Feb. 202143.0023.9913.2939.052.76−11.3838.0348.143.5933.356.7538.573.10Mar. 202116.0024.937.7019.953.4113.881.828.176.7543.1323.3920.433.82Apr. 202148.0025.8814.9444.052.673.0830.3558.447.0553.944.0143.572.99May. 202132.0026.843.9135.952.9911.1115.8319.069.8163.5423.8936.433.36Jun. 202133.0027.803.9129.052.9714.6713.7848.3111.5174.3331.0828.573.33Jul. 202123.0028.784.7026.953.21−41.1352.145.4714.2582.5048.3827.433.60Aug. 202133.0029.752.4429.052.97−20.3640.1252.5614.7182.2937.0628.573.33Sep. 202139.0030.745.9442.952.8415.7016.7717.6115.3976.5427.0143.433.19Oct. 202147.0031.7410.3843.052.6924.6915.1770.0015.6574.3618.6142.573.01Nov. 202142.0032.746.5245.952.7812.4820.7917.6217.1779.0226.0746.433.12Dec. 202140.0033.754.4736.052.82−140.81129.1565.5118.2288.8034.8635.573.17Jan. 202232.0034.762.0935.952.99−583.82466.535.6319.98106.1156.1436.433.36Feb. 202242.0035.794.3738.052.78−183.27158.6468.9718.9981.9928.1637.573.12Mar. 202258.0036.8213.4061.952.50−110.35106.5530.7217.2775.9011.3362.432.80Apr. 202235.0037.862.1231.052.93−90.7793.1662.3220.2471.6027.1130.573.28May. 202234.0038.913.6637.952.95−105.71104.266.9220.2170.0526.9038.433.31Jun. 202239.0039.970.7035.052.84−108.12105.8465.5619.1168.2221.0234.573.19Jul. 202213.0041.0324.8116.953.50−134.98130.95−12.7722.8066.8547.6617.433.92Aug. 202221.0042.1017.4417.053.27−47.6356.7245.7120.4261.1333.1616.573.66Sep. 202236.0043.185.2839.952.91−41.1756.7412.6017.2058.9916.9140.433.26MAPE (%)10.313.0959.3313.5426.173.14Oct. 202245.0044.270.5059.119.73−30.0551.76−43.6161.1156.467.9061.6811.50Nov. 202253.0045.374.993.2532.52−63.5576.18−74.7083.4661.355.4638.659.38MAPE (%)2.7421.1263.9772.296.6810.44Dec. 202246.4841.58−46.33−29.4959.2848.91Jan. 202347.5942.72−181.24−192.5357.2430.14Feb. 202348.7144.06−196.35−201.3555.269.50Table 11
Prediction results of travel sentiment in Thailand.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 20209.009.000.009.000.009.000.009.000.00Feb. 2020−2.0028.3130.93−2.490.5018.9621.38−2.670.69Mar. 2020−6.0029.2937.55−5.510.5220.9728.69−5.330.72Apr. 202025.0030.284.2324.510.3923.021.5824.330.54May. 202032.0031.280.5432.490.3725.155.1932.670.51Jun. 202036.0032.292.7335.510.3627.306.4035.330.49Jul. 202047.0033.309.3247.490.3329.4811.9247.670.46Aug. 202043.0034.326.0742.510.3431.717.9042.330.47Sep. 202036.0035.350.4836.490.3633.961.5036.670.49Oct. 202047.0036.397.2246.510.3336.267.3146.330.46Nov. 202050.0037.448.3850.490.3338.607.6050.670.45Dec. 202031.0038.495.7230.510.3740.717.4130.330.51Jan. 202149.0039.556.3449.490.3342.074.6549.670.45Feb. 202146.0040.623.6945.510.3444.870.7845.330.46Mar. 202151.0041.706.1651.490.3247.792.1251.670.4551.000.0051.000.00Apr. 202147.0042.782.8746.510.3345.471.0446.330.4650.442.3444.461.73May. 202153.0043.885.9653.490.3238.199.6853.670.4453.360.2455.541.66Jun. 202157.0044.987.6656.510.3137.8812.1856.330.4356.670.2154.461.62Jul. 202150.0046.092.6150.490.33−4.2436.1650.670.4561.777.8552.541.69Aug. 202143.0047.212.9442.510.34−60.6272.4642.330.4769.5418.5640.461.78Sep. 202155.0048.344.3055.490.32−30.3155.0455.670.4372.2111.1057.541.64Oct. 202145.0049.483.0944.510.34−18.1043.5244.330.4679.4323.7442.461.75Nov. 202152.0050.620.9152.490.320.5133.8752.670.4478.5017.4354.541.67Dec. 202160.0051.775.1459.510.3120.9024.4459.330.4278.5711.6157.461.59Jan. 202250.0052.941.9650.490.33−6.9137.9450.670.4582.5321.6852.541.69Feb. 202260.0054.113.6859.510.31−72.0482.5359.330.4287.8117.3857.461.59Mar. 202243.0055.298.5943.490.34−160.71142.4643.670.4796.1237.1445.541.78Apr. 202266.0056.485.7365.510.30−144.98127.1065.330.4095.9218.0263.461.53May. 202256.0057.681.0856.490.31−30.6655.5556.670.4388.3720.7558.541.63Jun. 202260.0058.890.6959.510.316.5133.4359.330.4285.4215.8957.461.59Jul. 202246.0060.119.6646.490.347.6726.2646.670.4686.1427.4948.541.74Aug. 202251.0061.336.8450.510.3213.0725.1250.330.4585.9423.1448.461.68Sep. 202253.0062.576.2553.490.3222.8519.7153.670.4485.5021.2455.541.66MAPE (%)6.340.3328.880.4615.571.58Oct. 202246.0063.8212.2033.018.8931.3610.039.7324.8484.9226.6678.9422.56Nov. 202259.0065.073.8230.2718.0731.5717.255.2733.7985.3416.5787.5317.94MAPE (%)8.0113.4813.6429.3221.6120.25Dec. 202266.3460.5633.5334.8385.5683.35Jan. 202367.6168.82−56.41−48.8993.7984.56Feb. 202368.8972.12−64.17−56.1494.1365.05Table 12
Prediction results of travel sentiment in Turkey.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 202019.0019.000.0019.000.00Feb. 2020−11.0010.8624.56−9.012.23Mar. 2020−34.0011.1268.37−35.993.01−34.000.00−34.000.00Apr. 202032.0011.3915.6133.991.5114.3613.3734.001.51May. 202025.0011.6610.6823.011.5915.317.7623.001.60Jun. 202011.0011.920.8312.991.7916.314.7813.001.80Jul. 20209.0012.192.937.011.8217.357.667.001.83Aug. 2020−4.0012.4617.14−2.012.0718.2923.22−2.002.08Sep. 202018.0012.734.4716.011.6819.181.0016.001.69Oct. 2020−13.0013.0029.88−11.012.2820.0337.97−11.002.30Nov. 202042.0013.2720.2340.011.4017.4717.2840.001.41Dec. 202014.0013.540.4115.991.74−7.5518.9016.001.75Jan. 202133.0013.8114.4331.011.4914.4913.9231.001.5033.000.0033.000.00Feb. 202114.0014.080.0715.991.7415.521.3316.001.7522.027.0314.550.48Mar. 202137.0014.3516.5335.011.455.5222.9835.001.4638.451.0536.450.40Apr. 202111.0014.633.2712.991.79−21.2329.0313.001.8051.0936.1211.550.49May. 20218.0014.906.396.011.845.851.996.001.8552.1140.857.450.51Jun. 202135.0015.1814.6836.991.4713.3216.0637.001.4863.8621.3835.550.41Jul. 202121.0015.454.5919.011.649.249.7219.001.6566.7837.8320.450.45Aug. 2021−13.0015.7333.02−11.012.28−4.629.63−11.002.3066.7891.70−12.450.63Sep. 202145.0016.0020.0043.011.37−10.8438.5143.001.3860.2810.5444.450.38Oct. 202136.0016.2814.5037.991.46−18.2539.8938.001.4749.459.8936.550.40Nov. 202123.0016.565.2421.011.62−16.1831.8621.001.6242.2515.6522.450.45Dec. 202142.0016.8417.7243.991.40−15.2440.3144.001.4145.762.6542.550.39Jan. 202215.0017.121.8413.011.73−90.2991.5613.001.7451.6231.8414.450.48Feb. 202232.0017.4011.0633.991.51−117.58113.3234.001.5143.808.9432.550.42Mar. 202221.0017.682.7519.011.64−35.3246.5419.001.6526.484.5320.450.45Apr. 202211.0017.966.2712.991.79−3.5813.1313.001.8018.536.7811.550.49May. 20224.0018.2413.692.011.914.480.472.001.9214.8510.443.450.53Jun. 2022−4.0018.5223.46−2.012.074.699.05−2.002.0812.6617.35−3.450.57Jul. 2022−10.0018.8132.01−11.992.21−41.6735.19−12.002.2219.1232.35−10.550.61Aug. 202214.0019.094.4715.991.74−38.2945.8716.001.7514.350.3114.550.48Sep. 202218.0019.371.1716.011.68−7.3121.4516.001.699.397.3017.450.46MAPE (%)13.401.7324.641.6818.790.45Oct. 202232.0019.669.35−0.2124.404.1221.1223.766.246.9518.98−0.5224.63Nov. 202233.0019.959.81−27.1745.248.4218.4816.1212.699.9717.327.9818.81MAPE (%)9.5834.8219.809.4718.1521.72Dec. 202220.2342.839.486.1712.48−27.06Jan. 202320.5231.88−39.70−50.0511.54−33.12Feb. 202320.8121.87−42.67−62.9610.71−17.61Table 13
Prediction results of travel sentiment in UK.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 202015.0015.000.0015.000.0015.000.0015.000.00Feb. 202010.00−0.219.2810.270.24−1.8410.7611.090.99Mar. 2020−28.000.3939.43−28.270.37−1.0037.50−29.091.52Apr. 20206.000.994.736.270.25−0.265.917.091.03May. 2020−1.001.592.62−1.270.270.611.62−2.091.11Jun. 2020−2.002.204.28−1.730.271.533.60−0.911.12Jul. 20203.002.810.192.730.262.420.561.911.06Aug. 202023.003.4215.9223.270.223.2816.0324.090.89Sep. 202026.004.0417.4325.730.213.9217.5224.910.87Oct. 202010.004.664.8610.270.243.296.1011.090.99Nov. 202023.005.2814.4022.730.223.5715.8021.910.89Dec. 2020−18.005.9129.16−17.730.333.0425.66−16.911.33Jan. 2021−18.006.5429.93−18.270.331.2023.42−19.091.33−18.000.00−18.000.00Feb. 2021−14.007.1824.63−13.730.315.8223.05−12.911.27−7.837.17−12.471.78Mar. 20216.007.821.715.730.257.491.414.911.0319.1412.394.471.44Apr. 20217.008.461.377.270.258.871.758.091.0236.1927.288.531.43May. 202112.009.112.5811.730.249.781.9810.910.9849.1333.1610.471.37Jun. 202110.009.760.2210.270.249.120.8011.090.9953.3039.3611.531.39Jul. 202110.0010.410.389.730.244.724.808.910.9951.8538.058.471.39Aug. 202112.0011.070.8312.270.245.725.6013.090.9850.0133.9413.531.37Sep. 202113.0011.741.1212.730.245.286.8311.910.9746.0529.2511.471.35Oct. 202122.0012.407.8722.270.223.5115.1523.090.9051.8424.4623.531.25Nov. 202128.0013.0711.6627.730.214.1318.6526.910.8553.6720.0526.471.20Dec. 202113.0013.750.6613.270.24−9.7520.1314.090.9763.3844.5914.531.35Jan. 202224.0014.437.7223.730.22−26.8841.0422.910.8848.7019.9222.471.23Feb. 202217.0015.111.6217.270.23−1.9316.1818.090.9433.0913.7618.531.31Mar. 202217.0015.791.0316.730.23−9.4622.6115.910.9433.5614.1515.471.31Apr. 202224.0016.496.0624.270.224.3115.8825.090.8829.324.2925.531.23May. 202235.0017.1813.2034.730.2011.5717.3533.910.8122.849.0133.471.13Jun. 202221.0017.882.5821.270.2210.508.6722.090.9019.661.1022.531.26Jul. 2022−6.0018.5826.15−6.270.289.1416.11−7.091.1618.0925.63−7.531.63Aug. 20223.0019.2915.823.270.2615.2611.904.091.0613.7410.434.531.49Sep. 202219.0020.000.8418.730.2317.960.8717.910.9212.075.8317.471.29MAPE (%)9.100.2412.580.9919.711.30Oct. 202225.0020.723.4331.194.9513.928.8726.851.4816.696.6512.0510.36Nov. 202227.0021.444.38−7.2226.9418.486.71−9.6128.8315.459.100.7820.65MAPE (%)3.9015.957.7915.157.8715.50Dec. 202222.1627.4418.9126.2614.37−13.28Jan. 202322.8920.037.174.4713.44−25.23Feb. 202323.6219.707.004.5712.62−29.14Table 14
Prediction results of travel sentiment in the US.
DatesActualPhase IPhase IIPhase IIIGM (1, 1)F-GM (1, 1)GM (1, N)F-GM (1, N)GM (1, N)F-GM (1, N)PredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEPredictedAPEJan. 20209.009.000.009.000.009.000.009.000.00Feb. 202014.009.094.3013.100.79−0.7612.9531.6915.52Mar. 2020−25.009.7646.35−24.101.202.2536.33−42.6923.59Apr. 2020−2.0010.4412.69−2.900.923.115.2215.6918.05May. 20205.0011.115.825.900.865.500.48−12.6916.85Jun. 2020−1.0011.7912.92−1.900.916.737.8016.6917.87Jul. 20205.0012.487.125.900.861.373.46−12.6916.85Aug. 202010.0013.172.889.100.823.715.7227.6916.08Sep. 202023.0013.867.4323.900.736.5413.385.3114.38Oct. 202023.0014.566.8622.100.73−0.5319.1340.6914.38Nov. 202035.0015.2614.6235.900.67−33.0150.3817.3113.10Dec. 202033.0015.9612.8132.100.68−70.0477.4750.6913.3033.000.0033.000.00Jan. 2021−1.0016.6817.85−0.100.91−79.5179.30−18.6917.8713.7714.921.042.06Feb. 202134.0017.3912.4033.100.67−32.5449.6651.6913.2033.010.7432.341.24Mar. 202128.0018.117.7328.900.70−25.8142.0410.3113.8252.1918.9029.250.97Apr. 202125.0018.834.9324.100.72−29.6943.7542.6914.1566.2032.9624.200.64May. 202127.0019.565.8627.900.71−11.4530.289.3113.9369.1333.1727.340.27Jun. 202127.0020.295.2826.100.711.2620.2744.6913.9369.3533.3527.130.10Jul. 202119.0021.031.7119.900.75−20.0432.811.3114.8668.8141.8618.410.50Aug. 20219.0021.7711.728.100.82−102.27102.0826.6916.2368.7654.8210.050.96Sep. 202123.0022.520.3923.900.73−111.26109.155.3114.3870.2338.4021.531.20Oct. 202140.0023.2711.9539.100.64−73.4081.0057.6912.6468.2220.1641.871.34Nov. 202152.0024.0218.4152.900.59−81.8588.0634.3111.6472.8413.7149.771.46Dec. 202129.0024.783.2728.100.70−223.65195.8646.6913.7168.7630.8231.531.96Jan. 202223.0025.552.0723.900.73−783.78655.925.3114.3846.2118.8720.222.26Feb. 202227.0026.320.5426.100.71−213.76189.5744.6913.9355.6822.5929.972.34Mar. 202230.0027.092.2430.900.69−107.37105.6712.3113.6155.0319.2626.912.37Apr. 202229.0027.870.8828.100.70−120.73116.0746.6913.7154.7919.9932.142.43May. 202233.0028.653.2733.900.68−203.80178.0515.3113.3049.6912.5529.882.34Jun. 202225.0029.443.5524.100.72−243.02214.4242.6914.1545.9016.7228.032.42Jul. 20224.0030.2325.224.900.86−278.33271.47−13.6917.0143.4237.901.132.76Aug. 20228.0031.0321.327.100.83−250.91239.7325.6916.3842.0231.5029.2919.71Sep. 202232.0031.830.1332.900.68−208.99182.5714.3113.4043.798.9343.128.42MAPE (%)8.930.7498.7914.5523.732.63Oct. 202229.0032.642.8236.655.93−176.71159.46−144.26134.3144.9812.3932.252.52Nov. 202244.0033.457.32−0.4130.84−196.83167.25−241.77198.4540.722.2840.042.75MAPE (%)5.0718.39163.35166.387.342.64Dec. 202234.2720.94−247.15−234.5836.4513.51Jan. 202335.0929.88−396.86−415.0434.04−7.96Feb. 202335.9222.23−429.32−419.3532.57−9.22Several common grounds can be summarized from the prediction results from the top 10 destinations. First of all, the majority of the grey prediction models can fit in the real data well, despite the fact that data lengths vary from one country to another. This shows how flexible the grey prediction models are to changing data lengths and conditions in various countries. Second, on the one hand, the grey prediction model with incorporated COVID-19 and vaccinations might better reflect the real scenario. On the other hand, the hybrid prediction models, F-GM (1, 1) and F-GM (1,N), are more accurate than the original models in both of the model fitting and ex-post testing, nevertheless. There are, however, certain exceptions. The predictions for Italy and Mexico in particular showed extremely substantial fluctuations in the model fitting that simply accounted for the COVID-19 shock effect, despite the residual modification being applied. Finally, the development trend of travel sentiment had been deflected and even presented the opposite development trajectories by introducing different shock effects. Specifically, the pandemic exerted huge downward pressure on travel sentiment by only considering the shock effect of COVID-19 in Phase II. On the contrary, travel sentiment in most countries showed an increasing trend rather than a downward trend by considering the effects of COVID-19 and vaccination simultaneously in Phase III. Therefore, vaccine adoption plays an important role in fighting against COVID-19, and it contributes to tourism recovery.


## 5. Discussion and Conclusions

Affected by the pandemic, the global tourism industry has fallen into a trough and travel sentiment has depressed. Whether the tourism industry can overcome the impact of COVID-19 and how travel sentiment and confidence in tourism might be restored have become major issues. Since COVID-19 and vaccination have had a shock effect on travel sentiment, the future patterns in travel sentiment may deviate from the original developing trends. However, due to the short impact time of the relevant factors, especially vaccination, there might be insufficient data to construct a prediction model that complies with the statistical distribution assumptions. In order to address the aforementioned shortcomings and forecast travel sentiment globally as well as in the top 10 destinations, grey prediction models were used in this paper. In addition, it measured the shock effects of COVID-19 and vaccinations and predicted the potential outcomes of its adjustment in the forthcoming stage. To improve the prediction accuracy, Fourier series were used as a residual modification model combined with the original GM (1, 1) and GM (1,N) models. The main conclusions are as follows.First, due to the widespread pandemic, the global tourism industry faced catastrophic effects and travel sentiment fluctuated considerably during the sample period. On the one hand, the public has adapted to quarantines and strict pandemic prevention measures, and their fear of the pandemic has gradually decreased. On the other hand, medical research on COVID-19 appears to have mitigated the effects of the pandemic. Therefore, overall travel sentiment is increasing, and negative sentiment is decreasing, which is consistent with the previous studies [40, 46].Second, in all countries, COVID-19 has exerted more or less downward pressure on travel sentiment. After considering vaccination as a relevant variable, travel sentiment was shown to increase in proportion to vaccination rates. Because of the effectiveness of vaccination, it has enhanced tourists’ willingness to travel, thus improving their travel sentiment. Therefore, to enhance their capacity to manage the pandemic, governments should actively promote vaccination. This will also help boost travel sentiment and the recovery of tourism.Third, based on the prediction results and the MAPE, Fourier series as a residual modification model can improve prediction accuracy in combination with both the original GM (1, 1) model and the GM (1,N) model. Our results showed the effectiveness of the proposed F-GM (1, 1) model and F-GM (1, N) model under mechanism analysis in the case of shock disturbances from COVID-19 and vaccination.This paper mainly focused on travel sentiment forecasting in different countries by considering the shock effects of COVID-19 and vaccination. Although the predictive model is unsatisfactory in individual countries, the proposed model is competent for predictions considering the shock effects. However, the influence of shock disturbances remains challenging for any prediction model. Furthermore, the new developing trend will diverge from the previous one as a result of the shock effects. Future research will concentrate on how to quantify the deviation, which is the shock effect. Therefore, in future studies, the prediction model can be further improved to reduce the influence of shock disturbances on the predicted results. Besides the Fourier series, other approaches should be combined with grey prediction models to achieve better prediction performance, for example, by using Markov-chains and neural networks, which deserve further research.



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*Source: 7334544-2023-02-10.xml*