Time series analysis of Holt model and the ARIMA Model facing Covid-19

Abstract

Background: Since the first appearance of the novel coronavirus in Wuhan in December 2019, it has quickly swept the world and become a major security incident facing humanity today. While the novel coronavirus threatens people’s lives and safety, the economies of various countries have also been severely damaged. Due to the epidemic, a large number of enterprises have faced closures, employment has become more difficult, and people’s lives have been greatly affected. Therefore, to establish a time series model for Hubei Province, where the novel coronavirus first broke out, and the United States, where the epidemic is most severe, to analyze the spreading trend and short-term forecast of the new coronavirus, which will help countries better understand the development trend of the epidemic and make more adequate preparation and timely intervention and treatment to prevent the further spread of the virus.
Methods: For the data collected from Hubei Province, including cumulative diagnoses, cumulative deaths, and cumulative cures, we use SPSS to establish the time series model. Since there is no problem of missing data values, we define days as the time variable, remove outliers, and set the width of the confidence interval to 95% for prediction, then use SPSS’s expert modeler to find the best-fit model for each sequence. ACF, PACF graphs of the residuals, and Q-tests are used to determine whether the residuals are white noise sequences and to check whether the model is a suitable model. Holt model is used for the cumulative number of diagnoses, and ARIMA (1,2,0) model is used for cumulative cures and deaths. Similarly, we also collect data for the US, including the cumulative number of diagnoses, cumulative deaths, and cumulative cures. For the three groups mentioned above, ARIMA (2,2,6) model, ARIMA (0,2,0) model, and ARIMA (0,2,1) model are used respectively.
Findings: From our modeling of the data, the time series diagrams of the real the fitted data almost overlap, so the fitting effect of the Holt model and the ARIMA model we use is very suitable. We compare the predicted values with the real values of the same period and find that the epidemic situation in Hubei Province has basically ended after May, but the epidemic situation in the United States has become more severe after May, so the Holt model and the ARIMA model are also very appropriate in predicting the epidemic situation in short-term.
Interpretation: Because the Chinese government has always put the safety of people ’s lives in the first place, when the epidemic broke out, it decisively closed the city of Hubei Province. One side is in trouble, all sides support, they concentrate all resources of whole country to save Hubei Province at the expense of the economy only in order to save more people. Now we can clearly see that the epidemic has been controlled in China and the whole country is developing in a good direction. The situation in the United States, on the other hand, is also influenced by the social environment.