Daily COVID-19 Variables in Nigeria: Are They Nonstationary, Long Memory or Interminable Long Memory Process?

S. A. Jibrin,Sani Salihu Abubakar and M. Samaila

Keywords: Long Memory, Interminable Long Memory, GPH test, Fractional differencing, ARFURIMA model and daily COVID-19 Variables in Nigeria


The secular trend, cyclical fluctuation, seasonal and irregular variations are common features of time series that may be observed by using the ordinary time plot graph. However, the time plot graph has the shortcomings of exposing other important components that hide in time series. The non-stationary, Long Memory (LM) and recently Interminable LM (ILM) are features that are seen using the Correlogram and confirmed using the unit root and LM tests. This study presents the Nigeria total sample of COVID-19 tested between 20th April and 6th May 2020, described the Nigeria daily COVID-19 new cases between 27th February and 4th May 2020, its active cases between 17th March and 4th May 2020, death rate between 6th April and 4th May 2020 and recovery rate between 18th March and 4th May 2020. The COVID-19 new cases, active cases, death rate and recovery rate variables were described using the time plot graph and Autocorrelation Function (ACF). The description results were further confirmed by using the Augmented Dickey-Fuller (ADF), Phillips-Perron (PP), Local Whittle Estimator (LWE) and Geweke and Porter-Hudak (GPH) tests. The results show that daily new COVID-19 cases are LM and have long memory estimate in the range of 0<d<1. Each of the COVID-19 active cases, death and recovery rate are non-stationary, ILM, produce differencing parameter approximately equal to unity (d=1) and fractional unit root difference values in the range of 1<d<2. Consequently, it was recommended that the Autoregressive Fractional Integral Moving Average (ARFIMA) model should be used for further analysis of daily COVID-19 new cases. Similarly, the Autoregressive Integral Moving Average (ARIMA) and Autoregressive Fractional Unit Root Integral Moving Average (ARFURIMA) models should be considered for modelling each of the COVID-19 active cases, death and recovery rate.