Ordinary least square and maximum likelihood estimation of VAR(1) model’s parameters and it’s application on covid-19 in China 2020

Abstract

Vector Autoregressive (VAR) is a multivariate time series model for examining objects with two or more variables in which the variables affect each other under the stationarity assumption. This study aims to compare the parameter estimation procedure of VAR(1) model of Ordinary Least Square (OLS) and Maximum Likelihood Estimation (MLE) methods. The comparison is investigated by both theoretical and empirical approaches. This study uses daily data of the number of positive cases and the number of deaths caused by covid-19 in China. Result shows that theoretically, the parameter estimation of OLS and MLE give the same results. Empirically, it is proven that the parameter estimation done by both methods provide the same results either in the presence and absence of intercept. For the presence of intercept, the number of positive cases influenced by both the number of positive cases itself and the number of deaths from the preceding period. Meanwhile, the number of deaths is only explained by the number of deaths in the previous period. For the absence of intercept, there is a significant effect of the number of positive cases from the previous period toward the number of positive cases, but the effect of the number of deaths in the preceding period is not significant. Hence, there is no effect of interaction between the number of positive cases and the number of deaths cases and vice versa.

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“…For high values of v, the Student's t distribution resembles the Gaussian distribution. For this reason we prefer to use a normal error, which in turn has other advantages [26][27][28], and is given by…”