# Exploring Time-Series Forecasting Models for Dynamic Pricing in Digital Signage Advertising
## 2 Review on Time-Series Forecasting Studies  
Time-series forecasting is used to predict future activities based on current historical data [9]. Commonly, the time-series data have the following characteristics: linearity, stationarity, and volatility. Linearity refers to the linear relationships of the time-series data to the time [10]. Stationary time-series data can be recognized as a property that does not depend on the time [11]. Generally, non-stationary time-series data include observations with trend and seasonality. The trend indicates the general movement of the data in each observed time frame without considering the data seasonality. Seasonality indicates a periodic fluctuation, which can be affected by time, magnitude, and direction. Volatility refers to the unexpected rise or fall of time-series data, which is also known as heteroscedasticity, where the time-series data variance comprises rapid changes between extremely high and low values [12]. As there are many available time-series forecasting models, the optimal model selection could be difficult. Thus, the above-mentioned data characteristics are essential in selecting an optimal time-series forecasting model, as the different models have different capabilities in handling different data characteristics. Apart from the three data characteristics, we included the size of the dataset as another consideration in selecting the optimal model, as it can influence the model performance, as will be seen shortly. The evolution of seven time-series forecasting models over the past two decades was studied to discover the popular models for dynamic pricing. Table 1 shows the listing of the studies. Figure 2 illustrates the distribution of the studies, showing the evolution of the model application in different domains. The Autoregressive Integrated Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) regression models, as a subcategory of the statistical models, have been applied since 2003. The regression model applications spanned over two decades. Stochastic models, such as Hidden Markov Model (HMM), have been used since 2007. The application of this model does not show any spike during the studied period. However, it was noted that the application of both regression and stochastic models were enhanced or combined with other approaches, such as the AI model, into the hybrid models starting from the 2010s to complement its shortcomings. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Category** & **Model** & **Count** & **Time Range** & **References** \\ \hline \multirow{2}{*}{**Regression Model**} & ARIMA & 14 & 2003–2019 & [13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27] \\  & GARCH & 9 & 2005–2021 & [12; 28; 29; 30; 31; 32; 33; 34; 35] \\ \hline \multirow{2}{*}{**Stochastic Model**} & HMM & 8 & 2007–2016 & [36; 37; 38; 39; 40; 41; 42; 43] \\ \hline \multirow{2}{*}{**Machine Learning**} & SVM & 12 & 2005–2021 & [44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61] \\  & RF & 6 & 2006–2021 & [62; 63; 64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 75; 76; 77; 78; 79; 80; 81; 82; 83; 84; 85; 86; 87; 88; 89; 90; 91; 92; 93] \\ \hline \multirow{2}{*}{**Deep Learning**} & ANN & 10 & 2004–2020 & [62; 63; 64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 76; 77; 78; 79; 80; 82; 83; 84; 86; 87; 88; 89; 91; 80; 83; 85; 87; 86; 88; 88; 89; 92; 80; 87; 88; 89; 93] \\  & RNN & 12 & 2006–2020 & [71; 81; 82; 83] \\ \hline \multirow{4}{*}{**Hybrid Model**} & Regression + Stochastic & 1 & 2017 & [83] \\  & Regression + ML & 4 & 2005–2021 & [84; 85; 86; 87; 88; 89; 90; 84; 87; 88; 85; 89; 86; 87; 88; 87; 89; 91; 80; 88; 89; 80; 89; 81; 82; 84; 83; 85; 86; 87; 88; 89; 82; 88; 89; 80; 81; 82; 85; 89; 80 Machine Learning (ML) models (of the AI models) have been applied since 2006, including Random Forest (RF) and Support Vector Machine (SVM). It was noted that these approaches were becoming more widespread in the 2010s as AI receives more attention.