[论文解读] Time Series Analysis and Forecasting of COVID-19 Cases Using LSTM and ARIMA Models

Arko Barman|arXiv (Cornell University)|Jun 5, 2020

COVID-19 diagnosis using AI参考文献 15被引用 10

一句话总结

本研究比较了长短期记忆网络（LSTM）与ARIMA模型在使用时间序列数据预测每日累计COVID-19病例数方面的表现。研究引入了新颖的k期评估指标——k日平均百分比误差（kMAPE）与k日中位对称准确率（kMdSA），发现两种模型表现相当，LSTM的kMAPE为0.05%，ARIMA为0.07%，表明其在公共卫生规划中具有极高的预测准确性。

ABSTRACT

Coronavirus disease 2019 (COVID-19) is a global public health crisis that has been declared a pandemic by World Health Organization. Forecasting country-wise COVID-19 cases is necessary to help policymakers and healthcare providers prepare for the future. This study explores the performance of several Long Short-Term Memory (LSTM) models and Auto-Regressive Integrated Moving Average (ARIMA) model in forecasting the number of confirmed COVID-19 cases. Time series of daily cumulative COVID-19 cases were used for generating 1-day, 3-day, and 5-day forecasts using several LSTM models and ARIMA. Two novel k-period performance metrics - k-day Mean Absolute Percentage Error (kMAPE) and k-day Median Symmetric Accuracy (kMdSA) - were developed for evaluating the performance of the models in forecasting time series values for multiple days. Errors in prediction using kMAPE and kMdSA for LSTM models were both as low as 0.05%, while those for ARIMA were 0.07% and 0.06% respectively. LSTM models slightly underestimated while ARIMA slightly overestimated the numbers in the forecasts. The performance of LSTM models is comparable to ARIMA in forecasting COVID-19 cases. While ARIMA requires longer sequences, LSTMs can perform reasonably well with sequence sizes as small as 3. However, LSTMs require a large number of training samples. Further, the development of k-period performance metrics proposed is likely to be useful for performance evaluation of time series models in predicting multiple periods. Based on the k-period performance metrics proposed, both LSTMs and ARIMA are useful for time series analysis and forecasting for COVID-19.

研究动机与目标

• 评估LSTM与ARIMA模型在每日累计COVID-19病例数据上的预测性能。
• 开发并应用新型k期评估指标——kMAPE与kMdSA，用于多日时间序列预测。
• 评估模型在不同序列长度下的鲁棒性，特别是小样本训练序列下的表现。
• 通过准确的短期病例预测，为公共卫生政策制定者提供可操作的见解。

提出的方法

• 将每日累计确诊COVID-19病例的时间序列数据作为LSTM与ARIMA模型的输入。
• LSTM模型在不同长度的序列上进行训练，包括最短3天的序列，以评估其在数据有限情况下的表现。
• ARIMA模型通过标准时间序列识别与选择程序拟合，基于AIC及自相关函数/偏自相关函数（ACF/PACF）分析确定模型参数。
• 引入kMAPE与kMdSA指标，用于评估连续k天内的预测准确性，从而改进多步预测的评估方法。
• 在多个国家的1天、3天与5天预测中评估模型性能。
• 采用超参数调优与交叉验证方法，以优化LSTM结构与ARIMA模型阶数选择。

实验结果

研究问题

• RQ1 LSTM与ARIMA模型在1天、3天与5天预测时间范围内的每日累计COVID-19病例预测表现如何比较？
• RQ2 与ARIMA相比，LSTM能否在极短输入序列（如3天）下实现可靠的预测？
• RQ3 所提出的kMAPE与kMdSA指标在评估多日预测性能方面有多有效？
• RQ4 与ARIMA相比，LSTM是否持续低估或高估病例数？
• RQ5 训练样本大小对LSTM与ARIMA预测准确率的影响如何？

主要发现

• LSTM模型在多日预测中实现了0.05%的kMAPE与0.05%的kMdSA，表明其预测精度极高。
• ARIMA模型的kMAPE为0.07%，kMdSA为0.06%，表现略低于LSTM。
• LSTM对病例数有轻微低估，而ARIMA则有轻微高估。
• 即使输入序列短至3天，LSTM仍表现出色，显示出对有限数据的强鲁棒性。
• 所提出的k期指标（kMAPE与kMdSA）在评估多步预测性能方面表现有效。
• 两种模型在公共卫生时间序列预测中均具可行性，LSTM在精度与灵活性方面略占优势。