Statistical Analysis of the Dynamics of Coronavirus Cases using Stepwise Switching Regression
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STATISTICAL ANALYSIS OF THE DYNAMICS OF CORONAVIRUS CASES USING STEPWISE SWITCHING REGRESSION P. S. Knopov1 and A. S. Korkhin2
UDC 519.233.5
Abstract. The dynamics of coronavirus cases is proposed to be modeled using switching regression whose switching points are unknown. The stepwise process of constructing the regression in time is described. The dynamics of the number of coronavirus cases in Ukraine is analyzed. Keywords: regression, switching points, regression parameters, stepwise estimation, infection, coronavirus. INTRODUCTION Switching regression is a set of regression models arranged sequentially in time, which can be both not related or related to each other. Regressions are divided one from another by switching points, which are often unknown. This case is a subject of the study. Noteworthy are the studies by P. Perron with co-authors (see, for example, [1–3]). They propose to use the Bellman and Roth algorithm [4] for estimation of switching points by the dynamic programming method. Developments by Perron and his co-authors were used to solve economic problems. The authors of the present paper also propose a number of results in generating switching regressions. The studies [5, 6] describe the methods of estimating switching points based on the given sampling, which allow taking into account the constraints imposed on these switching points and regression parameters that follow from the a priori information about the process being modeled. Such constraints cannot be taken into account when a dynamic programming scheme is used. In some applications (for example, economy, public health services), the concept of a fixed observation interval, which is used in [1–3, 5, 6], is not always acceptable in view of continuous data renewal. As an example, we will consider the coronavirus infection process, which is of current concern. In the paper, we propose to analyze the infection dynamics based on the switching regression model and create the model by steps in time. The observation interval, whose length is fixed or increases in time, is divided into a sequence of rather short overlapping intervals I j , j = 1, 2, K , which a priori contain a small number of switching points, for example, no more than two. This considerably simplifies the problem of their estimation. 1. METHODOLOGY OF CREATING THE MODEL OF THE TIME SERIES OF CORONAVIRUS CASES Figure 1 (whose data are taken from [7]) shows a time series of the daily number of coronavirus cases (NCC) in Ukraine since April 12, 2020, when NCC level had an evident growth tendency. As is seen from the figure, the rate of NCC variation is not constant: it varies in time not only in the value but also in the sign. Therefore, it is expedient to 1
V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine, [email protected]. 2Pridneprovskaya Academy of Construction and Architecture, Dnipro, Ukraine, [email protected]. Translated from Kibernetika i Sistemnyi Analiz, No. 6, November–December, 2020, pp. 96–106. Original article s
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