# Do we really need Foundation Models for multi-step-ahead Epidemic Forecasting?

Mrinmoy Dey, Aprameyo Chakrabartty, Dhruv Sarkar, Tanujit Chakraborty

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Mrinmoy Dey, Aprameyo Chakrabartty, Dhruv Sarkar, Tanujit Chakraborty. Do we really need Foundation Models for multi-step-ahead Epidemic Forecasting?. NeurIPS Workshop on Time Series in the Age of Large Models, Dec 2024, Vancouver, British Columbia, Canada. hal-04965040

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# Do we really need Foundation Models for multi-step-ahead Epidemic Forecasting?

Mrinmoy Dey*

Aprameyo Chakrabarty*

IIT Kharagpur

IIT Kharagpur

mdey3368@kgpian.iitkgp.ac.in

aprameyo@kgpian.iitkgp.ac.in

Dhruv Sarkar*

Tanujit Chakraborty

IIT Kharagpur

Sorbonne University

dhruv.sarkar@kgpian.iitkgp.ac.in

tanujitisi@gmail.com

## Abstract

The emergence of Foundation Models has radically transformed the Deep Learning scene and also accelerated its adoption in other domains. In particular, Large Language Models (LLMs) are being used in many time series forecasting tasks including Epidemic Forecasting. While the adoption of a new technology is generally a good sign, we must be scientific in analysing the benefits of doing so. We try two LLMs used in time series forecasting and show that on average, they perform almost similar or marginally better to the very popular classical statistical method ARIMA when applied to epidemic forecasting. We have performed extensive experiments on many Epidemic Forecasting datasets and thoroughly validated our conclusion that we need Foundation Models like LLMs for Epidemic Forecasting for the growth of the field even if the benefits are not proportionate to the costs immediately.

## 1 Introduction

Despite the recent surge in interest and investment into Foundation Models like LLMs, their application in domains outside of natural language processing remains an open question. LLMs have demonstrated remarkable abilities in language generation, translation, and understanding, but transferring these strengths to other domains such as time series forecasting, specifically epidemic forecasting, presents several challenges. Foremost among these are the domain-specific nuances that LLMs may fail to capture, particularly when handling epidemiological data that follows complex and irregular patterns unlike textual sequences.

Classical statistical models, such as ARIMA [1], and machine learning-based approaches, including Long Short-Term Memory (LSTM) [2] and Temporal Convolutional Networks (TCNs) [3], have been traditionally applied to time series forecasting problems. These models have proven robust and efficient, even with comparatively lower computational costs. In contrast, the computational resources required to fine-tune and deploy LLMs on such tasks are substantial. Not only do these models demand vast amounts of data and computing power, but their interpretability and reliability in the context of epidemic forecasting remain questionable. All these factors naturally provoke some cynicism regarding the applicability of LLMs in domain-specific tasks.

In this work, we aim to rigorously assess whether LLMs offer any real advantages over traditional statistical and machine learning models for epidemic forecasting. We believe that despite the

<footnote>*Equal contribution</footnote>
growing allure of using sophisticated models for every task, there are instances where simplicity can
outperform complexity. Through a series of comprehensive experiments across multiple epidemic
datasets, we evaluate the efficacy of popular LLMs when compared to baseline statistical models.

Our findings reveal that LLMs are marginally better than traditional methods of epidemic forecasting based on evaluations across many different datasets and using different metrics. Ultimately, this study seeks to answer the fundamental question: Do we really need Foundation Models for Epidemic Forecasting, or are traditional methods more suitable for this critical task?

The remainder of this paper is organized as follows: In Section 2, we review the background and related work on epidemic forecasting and the role of deep learning models, particularly LLMs. Section 3 details our experimental setup, including datasets, models, and evaluation metrics. Section 4 presents our results and analysis. Finally, Section 5 concludes the paper with our recommendations and potential future directions for epidemic forecasting research.

2 Related Work

2.1 Epidemic Forecasting: Challenges and Methods

Traditional approaches to epidemic forecasting have relied heavily on statistical models[4]. These
models include auto-regressive integrated moving average (ARIMA)[5], exponential smoothing[6],
and compartmental models such as the SIR (Susceptible-Infectious-Recovered) model [7] and its
variations. While these methods have proven to be useful in short-term forecasting, they often struggle
to capture long-range dependencies and the intricate, nonlinear nature of disease transmission in
real-world scenarios[8].

Recent advances in machine learning and deep learning have led to the application of more sophis-
ticated models to epidemic forecasting. Techniques such as Long Short-Term Memory (LSTM)
networks [9], Temporal Convolutional Networks (TCNs)[10], and hybrid models combining statistical
and machine learning approaches have shown promise in capturing the temporal dependencies and
complex patterns present in epidemic data. These models have provided notable improvements over
traditional methods, especially in medium- to long-term forecasts where patterns in the data are more
intricate[8].

## 2.2 The Rise of Large Language Models (LLMs) and Foundation Models

The central idea behind the use of LLMs in time series tasks is that sequences of data, whether they be words or numerical measurements, share some structural similarities. Like sentences in a language, time series data points can be viewed as temporally dependent, following certain patterns. Consequently, LLMs, with their strong sequence modelling capabilities, have been adapted for tasks beyond NLP, including financial forecasting[11], traffic accident forecasting[12], agricultural meteorological recommendations[13], and epidemic forecasting.

Despite their versatility, LLMs come with several limitations when applied outside of their native NLP domain[14]. They require large amounts of data for training and fine-tuning, making them resource-intensive. Additionally, their black-box nature raises concerns regarding interpretability, which is a crucial factor in high-stakes fields such as public health. While LLMs have shown promise in general time series forecasting tasks[15], their performance in specific, highly nuanced domains such as epidemic forecasting remains underexplored.

3 Experiments

The experiments were conducted on 15 epidemic forecasting datasets. Four of these datasets com-
prised monthly data, while the remaining 11 were composed of weekly data points. The models
were evaluated on short-term, medium-term, and long-term forecasting tasks. For the short-term
forecast, the evaluation period was set to 12 weeks for weekly and 6 months for monthly datasets.
For medium-term forecasting, this extended to 26 weeks and 12 months, respectively. For long-term
forecasting, the models were tested over 52 weeks for weekly and 24 months for monthly datasets.
We compared the performance of two large language models (LLMs), Chronos[16] and GTT[17],
against the ARIMA model across these datasets. The tables of the experiments and the definitions of the performance metrics (MSE, NRMSE, sMAPE, MASE) are given in the appendix below.

# 4 Results

In all the plots, a lower value in the y-axis indicates better performance, as all these metrics quantify error.

<figure><img src="image_3.png" /><figcaption>Figure 1: Average MSE performance</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 2: Average NRMSE performance</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Figure 3: Average sMAPE performance</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Figure 4: Average MASE performance</figcaption></figure>

5 Conclusion

In this paper, we explored whether Foundation Models like LLMs are necessary for Epidemic
Forecasting. Contrary to our initial expectations, we found that LLMs outperformed traditional
statistical methods and machine learning models. While concerns about their computational cost
are valid, the improved accuracy and generalization across diverse epidemic datasets suggest that
the benefits of LLMs can justify their use in many cases. Our results demonstrate that LLMs hold
significant potential for advancing epidemic forecasting, especially in scenarios demanding high
precision and adaptability.
References

[1] Soheila Mehrmolaei and Mohammad Reza Keyvanpour. Time series forecasting using improved arima. In *2016 Artificial Intelligence and Robotics (IRANOPEN)*, pages 92–97, 2016.

[2] Sima Siami-Namini, Neda Tavakoli, and Akbar Siami Namin. A comparison of arima and lstm in forecasting time series. In *2018 17th IEEE International Conference on Machine Learning and Applications (ICMLA)*, pages 1394–1401, 2018.

[3] Pedro Lara-Benítez, Manuel Carranza-García, José M Luna-Romera, and José C Riquelme. Temporal convolutional networks applied to energy-related time series forecasting. *applied sciences*, 10(7):2322, 2020.

[4] Igor Nesteruk. Statistics-based predictions of coronavirus epidemic spreading in mainland china. 2020.

[5] Alok Kumar Sahai, Namita Rath, Vishal Sood, and Manvendra Pratap Singh. Arima modelling & forecasting of covid-19 in top five affected countries. *Diabetes & metabolic syndrome: clinical research & reviews*, 14(5):1419–1427, 2020.

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[7] Agus Kartono, Savira Vita Karimah, Setyanto Tri Wahyudi, Ardian Arif Setiawan, and Ir-mansyah Sofian. Forecasting the long-term trends of coronavirus disease 2019 (covid-19) epidemic using the susceptible-infectious-recovered (sir) model. *Infectious Disease Reports*, 13(3):668–684, 2021.

[8] Sima Siami-Namini, Neda Tavakoli, and Akbar Siami Namin. A comparison of arima and lstm in forecasting time series. In *2018 17th IEEE international conference on machine learning and applications (ICMLA)*, pages 1394–1401. Ieee, 2018.

[9] Osman Tayfun Bişkin. Multi-step forecasting of covid-19 cases in european countries using temporal convolutional networks. *Mugla Journal of Science and Technology*, 7(1):117–126, 2021.

[10] Naoki Masuda and Petter Holme. Predicting and controlling infectious disease epidemics using temporal networks. *F1000prime reports*, 5, 2013.

[11] Huaqin Zhao, Zhengliang Liu, Zihao Wu, Yiwei Li, Tianze Yang, Peng Shu, Shaochen Xu, Haixing Dai, Lin Zhao, Gengchen Mai, et al. Revolutionizing finance with llms: An overview of applications and insights. *arXiv preprint arXiv:2401.11641*, 2024.

[12] Irene de Zarzà, Joachim de Curtò, Gemma Roig, and Carlos T Calafate. Llm multimodal traffic accident forecasting. *Sensors*, 23(22):9225, 2023.

[13] Ji-jun Park and Soo-joon Choi. Llms for enhanced agricultural meteorological recommendations. *arXiv preprint arXiv:2408.04640*, 2024.

[14] Muhammad Usman Hadi, Rizwan Qureshi, Abbas Shah, Muhammad Irfan, Anas Zafar, Muhammad Bilal Shaikh, Naveed Akhtar, Jia Wu, Seyedali Mirjalili, et al. A survey on large language models: Applications, challenges, limitations, and practical usage. *Authorea Preprints*, 2023.

[15] Mingyu Jin, Hua Tang, Chong Zhang, Qinkai Yu, Chengzhi Liu, Suiyuan Zhu, Yongfeng Zhang, and Mengnan Du. Time series forecasting with llms: Understanding and enhancing model capabilities. *arXiv preprint arXiv:2402.10835*, 2024.

[16] Abdul Fatir Ansari, Lorenzo Stella, Caner Turkmen, Xiyuan Zhang, Pedro Mercado, Huibin Shen, Oleksandr Shchur, Syama Sundar Rangapuram, Sebastian Pineda Arango, Shubham Kapoor, Jasper Zschiegner, Danielle C. Maddix, Hao Wang, Michael W. Mahoney, Kari Torkkola, Andrew Gordon Wilson, Michael Bohlke-Schneider, and Yuyang Wang. Chronos: Learning the language of time series, 2024.
[17] Cheng Feng, Long Huang, and Denis Krompass. Only the curve shape matters: Training foundation models for zero-shot multivariate time series forecasting through next curve shape prediction, 2024.

# A Appendix

## Performance Metrics

### Mean Squared Error (MSE)

The Mean Squared Error (MSE) is defined as:

$$MSE = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2$$

where $y_i$ is the actual value and $\hat{y}_i$ is the predicted value.

### Normalized Root Mean Squared Error (NRMSE)

The Normalized Root Mean Squared Error (NRMSE) is defined as:

$$NRMSE = \frac{\sqrt{\frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2}}{range(y)}$$

where $range(y) = max(y) - min(y)$ is the range of the actual values, $y_i$ is the actual value and $\hat{y}_i$ is the predicted value.

### Mean Absolute Scaled Error (MASE)

The Mean Absolute Scaled Error (MASE) is defined as:

$$MASE = \frac{\frac{1}{n} \sum_{i=1}^{n} |y_i - \hat{y}_i|}{\frac{1}{n-1} \sum_{i=2}^{n} |y_i - \hat{y}_{i-1}|}$$

where the denominator is the mean absolute error of a naive forecast, $y_i$ is the actual value and $\hat{y}_i$ is the predicted value.

### Symmetric Mean Absolute Percentage Error (SMAPE)

The Symmetric Mean Absolute Percentage Error (SMAPE) is defined as:

$$SMAPE = \frac{1}{n} \sum_{i=1}^{n} \frac{|y_i - \hat{y}_i|}{\frac{|y_i| + |\hat{y}_i|}{2}} \times 100\%$$

where $y_i$ is the actual value and $\hat{y}_i$ is the predicted value.

## Tables

The tables of data are given here

Tables of average of short, medium and length predictions
<table><caption>Table 1: MSE Average Performance of GTT, Chronos, and ARIMA on Different Datasets</caption><thead><tr><th>Datasets</th><th>GTT (Avg)</th><th>Chronos (Avg)</th><th>ARIMA (Avg)</th></tr></thead><tbody><tr><td>Ahmedabad_Dengue</td><td>122.6004</td><td>143.6623</td><td>207.1183</td></tr><tr><td>Bangkok_Dengue</td><td>740825.7504</td><td>275728.3536</td><td>8550124.604</td></tr><tr><td>Columbia_Dengue</td><td>652858.6193</td><td>475264.3818</td><td>580755.9641</td></tr><tr><td>Hong_Kong_Dengue</td><td>13.8348</td><td>19.9225</td><td>14.446</td></tr><tr><td>Iquitos_Dengue</td><td>184.3089</td><td>145.5153</td><td>119.4936</td></tr><tr><td>Philippines_Dengue</td><td>1596.7497</td><td>1881.6994</td><td>1706.9289</td></tr><tr><td>Sanjuan_Dengue</td><td>9047.1206</td><td>11499.1600</td><td>6382.6534</td></tr><tr><td>Singapore_Dengue</td><td>33718.4547</td><td>31537.8512</td><td>40336.3723</td></tr><tr><td>Venezuela_Dengue</td><td>464906.4173</td><td>338874.0402</td><td>401445.7626</td></tr><tr><td>China_Hepatitis_B</td><td>63755587.85</td><td>71747238.59</td><td>83331279.89</td></tr><tr><td>Australia_Influenza</td><td>5151.4435</td><td>1850.9421</td><td>5287.3691</td></tr><tr><td>Japan_Influenza</td><td>8167.124</td><td>4725.788</td><td>15093.8094</td></tr><tr><td>Mexico_Influenza</td><td>862.9881</td><td>662.4614</td><td>9334.4113</td></tr><tr><td>Colombia_Malaria</td><td>327205.35</td><td>253106.5358</td><td>321406.2418</td></tr><tr><td>Venezuela_Malaria</td><td>34424.3747</td><td>212854.3003</td><td>90574.99003</td></tr></tbody></table>

<table><caption>Table 2: NRMSE (Normalized Root Mean Square Error) Averages for Short Term, Medium Term, and Long Term Predictions across Datasets</caption><thead><tr><th>Datasets</th><th>GTT (Avg)</th><th>Chronos (Avg)</th><th>ARIMA (Avg)</th></tr></thead><tbody><tr><td>Ahmedabad_Dengue</td><td>0.64263</td><td>0.69180</td><td>0.31840</td></tr><tr><td>Bangkok_Dengue</td><td>0.95577</td><td>0.62730</td><td>1.33147</td></tr><tr><td>Columbia_Dengue</td><td>0.48413</td><td>0.44290</td><td>0.36627</td></tr><tr><td>Hong_Kong_Dengue</td><td>0.39377</td><td>0.45913</td><td>0.30797</td></tr><tr><td>Iquitos_Dengue</td><td>1.49687</td><td>1.06730</td><td>0.45653</td></tr><tr><td>Philippines_Dengue</td><td>0.66927</td><td>0.64290</td><td>0.29087</td></tr><tr><td>Sanjuan_Dengue</td><td>0.95823</td><td>1.11163</td><td>0.37060</td></tr><tr><td>Singapore_Dengue</td><td>0.55843</td><td>0.51633</td><td>0.42817</td></tr><tr><td>Venezuela_Dengue</td><td>0.51537</td><td>0.43363</td><td>0.41827</td></tr><tr><td>China_Hepatitis_B</td><td>0.08113</td><td>0.08517</td><td>0.38250</td></tr><tr><td>Australia_Influenza</td><td>0.76350</td><td>0.51673</td><td>0.28390</td></tr><tr><td>Japan_Influenza</td><td>8.44523</td><td>3.93940</td><td>1.20380</td></tr><tr><td>Mexico_Influenza</td><td>1.13933</td><td>1.56350</td><td>4.00750</td></tr><tr><td>Colombia_Malaria</td><td>0.39090</td><td>0.32340</td><td>0.31303</td></tr><tr><td>Venezuela_Malaria</td><td>0.11833</td><td>0.27893</td><td>0.50407</td></tr></tbody></table>

<table><caption>Table 3: sMAPE Average Values of Short Term, Medium Term, and Long Term Predictions across Datasets</caption><thead><tr><th>Datasets</th><th>GTT (Avg)</th><th>Chronos (Avg)</th><th>ARIMA (Avg)</th></tr></thead><tbody><tr><td>Ahmedabad_Dengue</td><td>61.35187</td><td>59.77397</td><td>85.16460</td></tr><tr><td>Bangkok_Dengue</td><td>75.18923</td><td>58.94240</td><td>88.70867</td></tr><tr><td>Columbia_Dengue</td><td>36.47127</td><td>38.32477</td><td>34.31167</td></tr><tr><td>Hong_Kong_Dengue</td><td>31.55783</td><td>38.20170</td><td>34.70473</td></tr><tr><td>Iquitos_Dengue</td><td>126.07760</td><td>127.92887</td><td>100.13343</td></tr><tr><td>Philippines_Dengue</td><td>50.17337</td><td>49.82253</td><td>53.09113</td></tr><tr><td>Sanjuan_Dengue</td><td>88.93157</td><td>86.92853</td><td>65.88140</td></tr><tr><td>Singapore_Dengue</td><td>38.38880</td><td>38.52190</td><td>45.42720</td></tr><tr><td>Venezuela_Dengue</td><td>49.06920</td><td>39.37093</td><td>45.52933</td></tr><tr><td>China_Hepatitis_B</td><td>6.25870</td><td>7.26393</td><td>7.32417</td></tr><tr><td>Australia_Influenza</td><td>73.28930</td><td>45.68120</td><td>64.65940</td></tr><tr><td>Japan_Influenza</td><td>116.47000</td><td>76.62087</td><td>122.62970</td></tr><tr><td>Mexico_Influenza</td><td>74.68967</td><td>81.07277</td><td>145.35950</td></tr><tr><td>Colombia_Malaria</td><td>34.59950</td><td>29.76523</td><td>33.27630</td></tr><tr><td>Venezuela_Malaria</td><td>9.01937</td><td>28.04663</td><td>17.96730</td></tr></tbody></table>
<table><caption>Table 4: MASE Average Values of Short Term, Medium Term, and Long Term Predictions across Datasets</caption><thead><tr><th>Datasets</th><th>GTT (Avg)</th><th>Chronos (Avg)</th><th>ARIMA (Avg)</th></tr></thead><tbody><tr><td>Ahmedabad_Dengue</td><td>1.94060</td><td>2.14977</td><td>2.98450</td></tr><tr><td>Bangkok_Dengue</td><td>3.13973</td><td>1.74447</td><td>7.31587</td></tr><tr><td>Columbia_Dengue</td><td>7.83080</td><td>6.67217</td><td>6.71217</td></tr><tr><td>Hong_Kong_Dengue</td><td>0.93920</td><td>0.95553</td><td>0.90003</td></tr><tr><td>Iquitos_Dengue</td><td>2.50020</td><td>1.96197</td><td>2.04223</td></tr><tr><td>Philippines_Dengue</td><td>1.01543</td><td>0.61387</td><td>0.75357</td></tr><tr><td>Sanjuan_Dengue</td><td>9.70020</td><td>10.67870</td><td>7.26073</td></tr><tr><td>Singapore_Dengue</td><td>4.99743</td><td>4.96997</td><td>5.65803</td></tr><tr><td>Venezuela_Dengue</td><td>5.69360</td><td>4.01090</td><td>5.31507</td></tr><tr><td>China_Hepatitis_B</td><td>0.81690</td><td>0.88130</td><td>0.89020</td></tr><tr><td>Australia_Influenza</td><td>5.38260</td><td>3.25907</td><td>5.48367</td></tr><tr><td>Japan_Influenza</td><td>1.09017</td><td>0.69210</td><td>1.78370</td></tr><tr><td>Mexico_Influenza</td><td>0.43457</td><td>0.49617</td><td>2.24700</td></tr><tr><td>Colombia_Malaria</td><td>3.66647</td><td>2.33897</td><td>2.82943</td></tr><tr><td>Venezuela_Malaria</td><td>1.18080</td><td>3.07593</td><td>2.02100</td></tr></tbody></table>
<table><caption>Table 5: Performance for Different Datasets and Prediction Ranges on MSE</caption><thead><tr><th>Datasets</th><th>Range</th><th>GTT</th><th>Chronos</th><th>ARIMA</th></tr></thead><tbody><tr><td>Ahmedabad_Dengue</td><td>Short Term</td><td>49.9611</td><td>79.3344</td><td>222.9468</td></tr><tr><td>Ahmedabad_Dengue</td><td>Medium Term</td><td>213.7265</td><td>248.0489</td><td>272.7149</td></tr><tr><td>Ahmedabad_Dengue</td><td>Long Term</td><td>104.1137</td><td>103.6036</td><td>127.6932</td></tr><tr><td>Bangkok_Dengue</td><td>Short Term</td><td>546469.3153</td><td>261267.6635</td><td>255629.9703</td></tr><tr><td>Bangkok_Dengue</td><td>Medium Term</td><td>123656.7008</td><td>226621.6852</td><td>192769.0608</td></tr><tr><td>Bangkok_Dengue</td><td>Long Term</td><td>1552351.235</td><td>337295.7122</td><td>25039824.78</td></tr><tr><td>Columbia_Dengue</td><td>Short Term</td><td>34576.6152</td><td>69252.4099</td><td>30045.2777</td></tr><tr><td>Columbia_Dengue</td><td>Medium Term</td><td>903659.5308</td><td>615275.3524</td><td>717175.1625</td></tr><tr><td>Columbia_Dengue</td><td>Long Term</td><td>1007339.712</td><td>743265.383</td><td>1013047.452</td></tr><tr><td>Hong_Kong_Dengue</td><td>Short Term</td><td>5.0303</td><td>8.2889</td><td>8.436</td></tr><tr><td>Hong_Kong_Dengue</td><td>Medium Term</td><td>14.5035</td><td>10.6096</td><td>15.1997</td></tr><tr><td>Hong_Kong_Dengue</td><td>Long Term</td><td>19.9706</td><td>38.8689</td><td>19.7023</td></tr><tr><td>Iquitos_Dengue</td><td>Short Term</td><td>153.8279</td><td>27.1052</td><td>84.244</td></tr><tr><td>Iquitos_Dengue</td><td>Medium Term</td><td>226.5892</td><td>270.2082</td><td>171.7012</td></tr><tr><td>Iquitos_Dengue</td><td>Long Term</td><td>174.5096</td><td>139.2326</td><td>102.5357</td></tr><tr><td>Philippines_Dengue</td><td>Short Term</td><td>670.0413</td><td>786.2015</td><td>483.9639</td></tr><tr><td>Philippines_Dengue</td><td>Medium Term</td><td>1602.4613</td><td>922.6166</td><td>1768.4554</td></tr><tr><td>Philippines_Dengue</td><td>Long Term</td><td>2515.7464</td><td>2936.2802</td><td>2868.3674</td></tr><tr><td>Sanjuan_Dengue</td><td>Short Term</td><td>7462.0006</td><td>13676.6681</td><td>952.1177</td></tr><tr><td>Sanjuan_Dengue</td><td>Medium Term</td><td>8476.4303</td><td>9409.2027</td><td>9476.8718</td></tr><tr><td>Sanjuan_Dengue</td><td>Long Term</td><td>11204.9309</td><td>11413.6093</td><td>8718.9706</td></tr><tr><td>Singapore_Dengue</td><td>Short Term</td><td>46268.1056</td><td>48427.2396</td><td>58239.5684</td></tr><tr><td>Singapore_Dengue</td><td>Medium Term</td><td>35179.4115</td><td>34621.0287</td><td>36844.9782</td></tr><tr><td>Singapore_Dengue</td><td>Long Term</td><td>19709.8469</td><td>11563.2852</td><td>25924.5703</td></tr><tr><td>Venezuela_Dengue</td><td>Short Term</td><td>629291.0722</td><td>479475.1294</td><td>557141.3027</td></tr><tr><td>Venezuela_Dengue</td><td>Medium Term</td><td>242586.9309</td><td>148171.6894</td><td>234704.0395</td></tr><tr><td>Venezuela_Dengue</td><td>Long Term</td><td>520841.2489</td><td>386977.3017</td><td>412491.9455</td></tr><tr><td>China_Hepatitis_B</td><td>Short Term</td><td>36264831.43</td><td>39770696.5</td><td>24107439.35</td></tr><tr><td>China_Hepatitis_B</td><td>Medium Term</td><td>95853695.84</td><td>123859614.3</td><td>136064376.8</td></tr><tr><td>China_Hepatitis_B</td><td>Long Term</td><td>59148236.27</td><td>53011404.96</td><td>89955023.53</td></tr><tr><td>Australia_Influenza</td><td>Short Term</td><td>192.9541</td><td>1434.0061</td><td>435.9705</td></tr><tr><td>Australia_Influenza</td><td>Medium Term</td><td>8640.1844</td><td>1548.5851</td><td>9841.2444</td></tr><tr><td>Australia_Influenza</td><td>Long Term</td><td>6621.0921</td><td>1568.235</td><td>5584.8924</td></tr><tr><td>Japan_Influenza</td><td>Short Term</td><td>11515.5003</td><td>4553.492</td><td>7938.3993</td></tr><tr><td>Japan_Influenza</td><td>Medium Term</td><td>8653.3359</td><td>652.7386</td><td>41.649</td></tr><tr><td>Japan_Influenza</td><td>Long Term</td><td>5282.5359</td><td>8969.1334</td><td>37301.38</td></tr><tr><td>Mexico_Influenza</td><td>Short Term</td><td>26.3165</td><td>243.1802</td><td>4723.1524</td></tr><tr><td>Mexico_Influenza</td><td>Medium Term</td><td>249.9592</td><td>429.3543</td><td>10556.6482</td></tr><tr><td>Mexico_Influenza</td><td>Long Term</td><td>2312.6887</td><td>1314.8496</td><td>12754.4334</td></tr><tr><td>Colombia_Malaria</td><td>Short Term</td><td>66999.9089</td><td>85176.543</td><td>92912.1633</td></tr><tr><td>Colombia_Malaria</td><td>Medium Term</td><td>252286.8395</td><td>58833.5159</td><td>270917.3322</td></tr><tr><td>Colombia_Malaria</td><td>Long Term</td><td>664329.3017</td><td>616310.5485</td><td>601389.2299</td></tr><tr><td>Venezuela_Malaria</td><td>Short Term</td><td>23921.4229</td><td>39633.5184</td><td>34978.9183</td></tr><tr><td>Venezuela_Malaria</td><td>Medium Term</td><td>43205.3772</td><td>238473.1437</td><td>174636.977</td></tr><tr><td>Venezuela_Malaria</td><td>Long Term</td><td>36146.324</td><td>358456.2389</td><td>62607.0748</td></tr></tbody></table>
<table><caption>Table 6: Performance on NRMSE for Different Datasets and Prediction Ranges</caption><thead><tr><th>Datasets</th><th>Range</th><th>GTT</th><th>Chronos</th><th>ARIMA</th></tr></thead><tbody><tr><td>Ahmedabad_Dengue</td><td>Short Term</td><td>0.372</td><td>0.4687</td><td>0.3732</td></tr><tr><td>Ahmedabad_Dengue</td><td>Medium Term</td><td>0.6861</td><td>0.7391</td><td>0.3514</td></tr><tr><td>Ahmedabad_Dengue</td><td>Long Term</td><td>0.8698</td><td>0.8676</td><td>0.2306</td></tr><tr><td>Bangkok_Dengue</td><td>Short Term</td><td>0.6173</td><td>0.4268</td><td>0.8426</td></tr><tr><td>Bangkok_Dengue</td><td>Medium Term</td><td>0.4578</td><td>0.6197</td><td>0.3532</td></tr><tr><td>Bangkok_Dengue</td><td>Long Term</td><td>1.7922</td><td>0.8354</td><td>2.7986</td></tr><tr><td>Columbia_Dengue</td><td>Short Term</td><td>0.1919</td><td>0.2716</td><td>0.2575</td></tr><tr><td>Columbia_Dengue</td><td>Medium Term</td><td>0.7578</td><td>0.6253</td><td>0.4952</td></tr><tr><td>Columbia_Dengue</td><td>Long Term</td><td>0.5027</td><td>0.4318</td><td>0.3461</td></tr><tr><td>Hong_Kong_Dengue</td><td>Short Term</td><td>0.2588</td><td>0.3322</td><td>0.363</td></tr><tr><td>Hong_Kong_Dengue</td><td>Medium Term</td><td>0.448</td><td>0.3832</td><td>0.2998</td></tr><tr><td>Hong_Kong_Dengue</td><td>Long Term</td><td>0.4745</td><td>0.662</td><td>0.2611</td></tr><tr><td>Iquitos_Dengue</td><td>Short Term</td><td>2.1262</td><td>0.8925</td><td>0.706</td></tr><tr><td>Iquitos_Dengue</td><td>Medium Term</td><td>0.9933</td><td>1.0847</td><td>0.3743</td></tr><tr><td>Iquitos_Dengue</td><td>Long Term</td><td>1.3711</td><td>1.2247</td><td>0.2893</td></tr><tr><td>Philippines_Dengue</td><td>Short Term</td><td>0.5056</td><td>0.5476</td><td>0.3267</td></tr><tr><td>Philippines_Dengue</td><td>Medium Term</td><td>0.7517</td><td>0.5703</td><td>0.299</td></tr><tr><td>Philippines_Dengue</td><td>Long Term</td><td>0.7505</td><td>0.8108</td><td>0.2469</td></tr><tr><td>Sanjuan_Dengue</td><td>Short Term</td><td>1.1739</td><td>1.5893</td><td>0.241</td></tr><tr><td>Sanjuan_Dengue</td><td>Medium Term</td><td>0.6589</td><td>0.6941</td><td>0.4613</td></tr><tr><td>Sanjuan_Dengue</td><td>Long Term</td><td>1.0419</td><td>1.0515</td><td>0.4095</td></tr><tr><td>Singapore_Dengue</td><td>Short Term</td><td>0.5201</td><td>0.532</td><td>0.5509</td></tr><tr><td>Singapore_Dengue</td><td>Medium Term</td><td>0.5846</td><td>0.5799</td><td>0.4382</td></tr><tr><td>Singapore_Dengue</td><td>Long Term</td><td>0.5706</td><td>0.4371</td><td>0.2954</td></tr><tr><td>Venezuela_Dengue</td><td>Short Term</td><td>0.5602</td><td>0.489</td><td>0.5985</td></tr><tr><td>Venezuela_Dengue</td><td>Medium Term</td><td>0.4714</td><td>0.3684</td><td>0.2902</td></tr><tr><td>Venezuela_Dengue</td><td>Long Term</td><td>0.5145</td><td>0.4435</td><td>0.3661</td></tr><tr><td>China_Hepatitis_B</td><td>Short Term</td><td>0.0612</td><td>0.064</td><td>0.3301</td></tr><tr><td>China_Hepatitis_B</td><td>Medium Term</td><td>0.1006</td><td>0.1143</td><td>0.4848</td></tr><tr><td>China_Hepatitis_B</td><td>Long Term</td><td>0.0816</td><td>0.0772</td><td>0.3326</td></tr><tr><td>Australia_Influenza</td><td>Short Term</td><td>0.2187</td><td>0.5963</td><td>0.1221</td></tr><tr><td>Australia_Influenza</td><td>Medium Term</td><td>0.8591</td><td>0.3637</td><td>0.4221</td></tr><tr><td>Australia_Influenza</td><td>Long Term</td><td>1.2127</td><td>0.5902</td><td>0.3075</td></tr><tr><td>Japan_Influenza</td><td>Short Term</td><td>11.8139</td><td>7.4289</td><td>3.0723</td></tr><tr><td>Japan_Influenza</td><td>Medium Term</td><td>12.8649</td><td>3.5333</td><td>0.2225</td></tr><tr><td>Japan_Influenza</td><td>Long Term</td><td>0.6569</td><td>0.856</td><td>0.3166</td></tr><tr><td>Mexico_Influenza</td><td>Short Term</td><td>0.5005</td><td>1.5213</td><td>4.5816</td></tr><tr><td>Mexico_Influenza</td><td>Medium Term</td><td>1.7418</td><td>2.2828</td><td>6.8497</td></tr><tr><td>Mexico_Influenza</td><td>Long Term</td><td>1.1757</td><td>0.8864</td><td>0.5912</td></tr><tr><td>Colombia_Malaria</td><td>Short Term</td><td>0.2663</td><td>0.3002</td><td>0.3113</td></tr><tr><td>Colombia_Malaria</td><td>Medium Term</td><td>0.4226</td><td>0.204</td><td>0.3294</td></tr><tr><td>Colombia_Malaria</td><td>Long Term</td><td>0.4838</td><td>0.466</td><td>0.2984</td></tr><tr><td>Venezuela_Malaria</td><td>Short Term</td><td>0.0953</td><td>0.1226</td><td>0.4832</td></tr><tr><td>Venezuela_Malaria</td><td>Medium Term</td><td>0.1292</td><td>0.3034</td><td>0.7475</td></tr><tr><td>Venezuela_Malaria</td><td>Long Term</td><td>0.1305</td><td>0.4108</td><td>0.2814</td></tr></tbody></table>
<table><caption>Table 7: Performance on sMAPE for Different Datasets and Prediction Ranges</caption><thead><tr><th>Datasets</th><th>Range</th><th>GTT</th><th>Chronos</th><th>ARIMA</th></tr></thead><tbody><tr><td>Ahmedabad_Dengue</td><td>Short Term</td><td>39.0617</td><td>42.4409</td><td>72.075</td></tr><tr><td>Ahmedabad_Dengue</td><td>Medium Term</td><td>72.5782</td><td>68.2738</td><td>74.1195</td></tr><tr><td>Ahmedabad_Dengue</td><td>Long Term</td><td>72.4157</td><td>68.6072</td><td>109.2993</td></tr><tr><td>Bangkok_Dengue</td><td>Short Term</td><td>83.0279</td><td>51.8012</td><td>46.3884</td></tr><tr><td>Bangkok_Dengue</td><td>Medium Term</td><td>48.9045</td><td>54.846</td><td>59.2161</td></tr><tr><td>Bangkok_Dengue</td><td>Long Term</td><td>95.6353</td><td>70.18</td><td>158.5215</td></tr><tr><td>Columbia_Dengue</td><td>Short Term</td><td>13.2665</td><td>29.4646</td><td>11.5341</td></tr><tr><td>Columbia_Dengue</td><td>Medium Term</td><td>55.4624</td><td>47.4629</td><td>50.2788</td></tr><tr><td>Columbia_Dengue</td><td>Long Term</td><td>40.6849</td><td>38.0468</td><td>41.1221</td></tr><tr><td>Hong_Kong_Dengue</td><td>Short Term</td><td>23.2743</td><td>25.5224</td><td>28.0633</td></tr><tr><td>Hong_Kong_Dengue</td><td>Medium Term</td><td>35.3415</td><td>26.1447</td><td>38.1541</td></tr><tr><td>Hong_Kong_Dengue</td><td>Long Term</td><td>36.0577</td><td>64.938</td><td>35.8968</td></tr><tr><td>Iquitos_Dengue</td><td>Short Term</td><td>116.8591</td><td>111.6716</td><td>103.729</td></tr><tr><td>Iquitos_Dengue</td><td>Medium Term</td><td>119.0524</td><td>154.0943</td><td>91.4318</td></tr><tr><td>Iquitos_Dengue</td><td>Long Term</td><td>144.3213</td><td>116.0207</td><td>105.2395</td></tr><tr><td>Philippines_Dengue</td><td>Short Term</td><td>28.7104</td><td>46.8799</td><td>29.6495</td></tr><tr><td>Philippines_Dengue</td><td>Medium Term</td><td>62.3573</td><td>41.5399</td><td>65.163</td></tr><tr><td>Philippines_Dengue</td><td>Long Term</td><td>59.4524</td><td>59.0478</td><td>64.4609</td></tr><tr><td>Sanjuan_Dengue</td><td>Short Term</td><td>78.9867</td><td>88.3057</td><td>38.6054</td></tr><tr><td>Sanjuan_Dengue</td><td>Medium Term</td><td>70.9519</td><td>69.6806</td><td>79.5502</td></tr><tr><td>Sanjuan_Dengue</td><td>Long Term</td><td>116.8561</td><td>100.7993</td><td>77.4886</td></tr><tr><td>Singapore_Dengue</td><td>Short Term</td><td>41.6264</td><td>43.3445</td><td>49.1369</td></tr><tr><td>Singapore_Dengue</td><td>Medium Term</td><td>35.6501</td><td>39.8697</td><td>37.9576</td></tr><tr><td>Singapore_Dengue</td><td>Long Term</td><td>37.8899</td><td>32.3515</td><td>49.1871</td></tr><tr><td>Venezuela_Dengue</td><td>Short Term</td><td>62.5424</td><td>52.286</td><td>56.556</td></tr><tr><td>Venezuela_Dengue</td><td>Medium Term</td><td>40.5451</td><td>26.6095</td><td>39.5521</td></tr><tr><td>Venezuela_Dengue</td><td>Long Term</td><td>46.1201</td><td>39.2173</td><td>40.4799</td></tr><tr><td>China_Hepatitis_B</td><td>Short Term</td><td>5.687</td><td>5.651</td><td>3.7298</td></tr><tr><td>China_Hepatitis_B</td><td>Medium Term</td><td>8.9179</td><td>10.5759</td><td>10.4198</td></tr><tr><td>China_Hepatitis_B</td><td>Long Term</td><td>6.1712</td><td>5.5649</td><td>7.8229</td></tr><tr><td>Australia_Influenza</td><td>Short Term</td><td>25.6069</td><td>40.8236</td><td>33.2323</td></tr><tr><td>Australia_Influenza</td><td>Medium Term</td><td>80.0547</td><td>35.157</td><td>90.6562</td></tr><tr><td>Australia_Influenza</td><td>Long Term</td><td>116.2063</td><td>61.063</td><td>70.0897</td></tr><tr><td>Japan_Influenza</td><td>Short Term</td><td>132.8153</td><td>113.9108</td><td>164.6492</td></tr><tr><td>Japan_Influenza</td><td>Medium Term</td><td>128.3771</td><td>60.8674</td><td>67.7042</td></tr><tr><td>Japan_Influenza</td><td>Long Term</td><td>88.2176</td><td>55.0844</td><td>135.5356</td></tr><tr><td>Mexico_Influenza</td><td>Short Term</td><td>49.0266</td><td>70.541</td><td>138.0216</td></tr><tr><td>Mexico_Influenza</td><td>Medium Term</td><td>83.1781</td><td>84.4798</td><td>163.1871</td></tr><tr><td>Mexico_Influenza</td><td>Long Term</td><td>91.8643</td><td>88.1975</td><td>134.8698</td></tr><tr><td>Colombia_Malaria</td><td>Short Term</td><td>24.3532</td><td>30.0795</td><td>23.9966</td></tr><tr><td>Colombia_Malaria</td><td>Medium Term</td><td>34.6083</td><td>16.8536</td><td>35.3094</td></tr><tr><td>Colombia_Malaria</td><td>Long Term</td><td>44.837</td><td>40.3626</td><td>40.5229</td></tr><tr><td>Venezuela_Malaria</td><td>Short Term</td><td>6.8467</td><td>11.1651</td><td>10.3734</td></tr><tr><td>Venezuela_Malaria</td><td>Medium Term</td><td>10.9895</td><td>32.171</td><td>26.5742</td></tr><tr><td>Venezuela_Malaria</td><td>Long Term</td><td>11.2219</td><td>42.8038</td><td>14.9543</td></tr></tbody></table>
<table><caption>Table 8: Performance on MASE for Different Datasets and Prediction Ranges</caption><thead><tr><th>Datasets</th><th>Range</th><th>GTT</th><th>Chronos</th><th>ARIMA</th></tr></thead><tbody><tr><td>Ahmedabad_Dengue</td><td>Short Term (Weekly)</td><td>1.3479</td><td>1.6204</td><td>3.3477</td></tr><tr><td>Ahmedabad_Dengue</td><td>Medium Term</td><td>2.8368</td><td>3.1959</td><td>3.4316</td></tr><tr><td>Ahmedabad_Dengue</td><td>Long Term</td><td>1.6371</td><td>1.6310</td><td>2.1742</td></tr><tr><td>Bangkok_Dengue</td><td>Short Term (Monthly)</td><td>2.6328</td><td>1.8479</td><td>1.7421</td></tr><tr><td>Bangkok_Dengue</td><td>Medium Term</td><td>1.1458</td><td>1.4177</td><td>1.4813</td></tr><tr><td>Bangkok_Dengue</td><td>Long Term</td><td>5.6406</td><td>1.9678</td><td>18.7242</td></tr><tr><td>Columbia_Dengue</td><td>Short Term (Weekly)</td><td>1.3202</td><td>2.8413</td><td>1.1234</td></tr><tr><td>Columbia_Dengue</td><td>Medium Term</td><td>10.2263</td><td>8.2198</td><td>8.9231</td></tr><tr><td>Columbia_Dengue</td><td>Long Term</td><td>9.9459</td><td>8.9554</td><td>10.0900</td></tr><tr><td>Hong_Kong_Dengue</td><td>Short Term (Monthly)</td><td>0.5897</td><td>0.6894</td><td>0.7362</td></tr><tr><td>Hong_Kong_Dengue</td><td>Medium Term</td><td>0.8737</td><td>0.6873</td><td>0.9563</td></tr><tr><td>Hong_Kong_Dengue</td><td>Long Term</td><td>1.3542</td><td>1.4899</td><td>1.0076</td></tr><tr><td>Iquitos_Dengue</td><td>Short Term</td><td>2.7141</td><td>1.0056</td><td>1.8842</td></tr><tr><td>Iquitos_Dengue</td><td>Medium Term</td><td>2.7717</td><td>3.1149</td><td>2.4476</td></tr><tr><td>Iquitos_Dengue</td><td>Long Term</td><td>2.0148</td><td>1.7654</td><td>1.7949</td></tr><tr><td>Philippines_Dengue</td><td>Short Term</td><td>0.3608</td><td>0.4879</td><td>0.3823</td></tr><tr><td>Philippines_Dengue</td><td>Medium Term</td><td>0.7726</td><td>0.5178</td><td>0.8298</td></tr><tr><td>Philippines_Dengue</td><td>Long Term</td><td>1.9129</td><td>0.8359</td><td>1.0486</td></tr><tr><td>Sanjuan_Dengue</td><td>Short Term</td><td>9.7748</td><td>12.6675</td><td>3.4368</td></tr><tr><td>Sanjuan_Dengue</td><td>Medium Term</td><td>9.2277</td><td>9.7126</td><td>10.0301</td></tr><tr><td>Sanjuan_Dengue</td><td>Long Term</td><td>10.0981</td><td>9.6560</td><td>8.3153</td></tr><tr><td>Singapore_Dengue</td><td>Short Term</td><td>6.5031</td><td>6.6971</td><td>7.3558</td></tr><tr><td>Singapore_Dengue</td><td>Medium Term</td><td>4.6416</td><td>4.9871</td><td>4.8633</td></tr><tr><td>Singapore_Dengue</td><td>Long Term</td><td>3.8476</td><td>3.2257</td><td>4.7550</td></tr><tr><td>Venezuela_Dengue</td><td>Short Term</td><td>6.9101</td><td>6.0295</td><td>6.4277</td></tr><tr><td>Venezuela_Dengue</td><td>Medium Term</td><td>4.2874</td><td>2.8156</td><td>4.1646</td></tr><tr><td>Venezuela_Dengue</td><td>Long Term</td><td>5.8833</td><td>5.1876</td><td>5.3529</td></tr><tr><td>China_Hepatitis_B</td><td>Short Term</td><td>0.7170</td><td>0.7119</td><td>0.4709</td></tr><tr><td>China_Hepatitis_B</td><td>Medium Term</td><td>1.0970</td><td>1.2798</td><td>1.2799</td></tr><tr><td>China_Hepatitis_B</td><td>Long Term</td><td>0.6367</td><td>0.6522</td><td>0.9198</td></tr><tr><td>Australia_Influenza</td><td>Short Term</td><td>1.2751</td><td>3.0448</td><td>1.7711</td></tr><tr><td>Australia_Influenza</td><td>Medium Term</td><td>8.2295</td><td>3.2642</td><td>9.1346</td></tr><tr><td>Australia_Influenza</td><td>Long Term</td><td>6.6432</td><td>3.4682</td><td>5.5453</td></tr><tr><td>Japan_Influenza</td><td>Short Term</td><td>1.3743</td><td>0.8516</td><td>1.6661</td></tr><tr><td>Japan_Influenza</td><td>Medium Term</td><td>0.9913</td><td>0.2269</td><td>0.0973</td></tr><tr><td>Japan_Influenza</td><td>Long Term</td><td>0.9049</td><td>0.9978</td><td>3.5877</td></tr><tr><td>Mexico_Influenza</td><td>Short Term</td><td>0.1166</td><td>0.3114</td><td>1.5686</td></tr><tr><td>Mexico_Influenza</td><td>Medium Term</td><td>0.3424</td><td>0.4197</td><td>2.4803</td></tr><tr><td>Mexico_Influenza</td><td>Long Term</td><td>0.8447</td><td>0.7574</td><td>2.6920</td></tr><tr><td>Colombia_Malaria</td><td>Short Term</td><td>1.3469</td><td>1.6643</td><td>1.3635</td></tr><tr><td>Colombia_Malaria</td><td>Medium Term</td><td>2.8422</td><td>1.1484</td><td>2.8980</td></tr><tr><td>Colombia_Malaria</td><td>Long Term</td><td>4.8103</td><td>4.2043</td><td>4.2268</td></tr><tr><td>Venezuela_Malaria</td><td>Short Term</td><td>0.8686</td><td>1.3838</td><td>1.2948</td></tr><tr><td>Venezuela_Malaria</td><td>Medium Term</td><td>1.3834</td><td>3.5803</td><td>3.0477</td></tr><tr><td>Venezuela_Malaria</td><td>Long Term</td><td>1.2904</td><td>4.2637</td><td>1.7205</td></tr></tbody></table>