How to determine whether the covid-19 infection series are stationary and can be predicted or whether they are non-stationary and cannot be predicted?

Abstract

Lopez-Gatell, who has managed the public policy to control the SARS-CoV-2 virus, has on several occasions made forecasts on the dynamics of infections and deaths; but if such series are non-stationary, this implies a very serious error. In our opinion, many of these series have a non-stationary data generating process and, therefore, forecasts cannot be made. To determine this, we will use various econometric techniques such as unit root tests and, in addition, we will see if the series responds to a regime shift process. As results we have that the series of weekly contagions by COVID-19 in 8 entities of the country, only one of them is stationary, in addition, when analyzing the trajectory of the contagions through Markov chains to determine the performance of these states to control the contagions, we found that one of them had a very bad performance, 5 with bad performance and 1 with good performance.