Analysis and prediction of confirmed COVID-19 cases in China with uncertain time series
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Analysis and prediction of confirmed COVID-19 cases in China with uncertain time series Tingqing Ye1 · Xiangfeng Yang2 Accepted: 7 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper presents an uncertain time series model to analyse and predict the evolution of confirmed COVID-19 cases in China, excluding imported cases. Compared with the results of the classical time series model, the uncertain time series model could better describe the COVID-19 epidemic by using an uncertain hypothesis test to filter out outliers. This improvement is reflected in the two observations. One is that the estimated variance of the disturbance term in the uncertain time series model is more appropriate and acceptable than that in the classical time series model, and the other is that the disturbance term of the classical time series model cannot be regarded as a random variable but as an uncertain variable. Keywords Uncertainty theory · Uncertain time series · Uncertain hypothesis test · COVID-19
1 Introduction COVID-19 has become a pandemic and a public health emergency. As of March 23, 2020, a total of 67,801 confirmed cases and 3160 deaths have been reported in mainland China. Respiratory droplets and human-to-human contact are the major routes of transmission of COVID-19. Based on initial confirmed COVID-19 cases, how can we model its evolution? There exist two mathematical methods: probabilistic statistics and uncertain statistics. The difference between probabilistic statistics and uncertain statistics is that the
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Xiangfeng Yang [email protected] Tingqing Ye [email protected]
1
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
2
School of Information Technology and Management, University of International Business and Economics, Beijing 100029, China
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T. Ye, X. Yang
former is in the framework of the probability theory, while the latter is in the structure of the uncertainty theory. Probability theory is a “multiplication” mathematical system, and uncertainty theory is a “minimum” mathematical system. The origin of uncertainty theory could be traced to the pioneering work of Liu (2007), who established uncertainty theory based on normality, duality, and subadditivity axioms. In addition, to address the product uncertain measure, Liu (2009) introduced the fourth axiom–product axiom of uncertainty theory. Since then, uncertainty theory has become an ideal mathematical system and has been applied in many fields. This paper will adopt an uncertain statistics methodology to interpret and analyse confirmed COVID-19 cases in China. Uncertain regression analysis as a field of uncertain statistics was first presented by Yao and Liu (2018). They applied the least squares method to estimating the parameters of the uncertain regression model. Later, Lio and Liu (2018) investigated the residual and confidence intervals in an uncertain regression model. As an extension of an uncertain regression model, a multivariate uncertain regress
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