Sanusi Alhaji Jibrin, Yakubu Musa , Mohammed Samaila and Ahmad Abdul

Keywords: Interminable long memory, GPH test, Fractional unit root differencing, ARFURIMA model and monthly stock price index

Abstract

Financial indices are known to exhibit an upward or downward trend and are classified as a non-stationary time series. Therefore, many stationary tests are used to investigate and confirmed the presence of a unit root in this type of series. The first differenced transformation method using (d=1) is used to obtain a stationary component of this series and the Autoregressive Integral Moving Average (ARIMA) model estimated. Also, another dwelled and unwanted component in the similar financial time series is a long memory and is determined by using the autocorrelation function, long memory tests and fractional ARIMA could be the appropriate model to study the series. In this paper, a monthly Nigeria stock index representing thirty (30) stock price indices (N30SPI) between the 29th January 2010 and 31st December 2018 were analyzed using the ARIMA and Autoregressive Fractional Unit Root Integral Moving Average (ARFURIMA) model. The Kwiatkowski-Phillips-Schmidt-Shin (KPSS) and Geweke and Porter-Hudak (GPH) test results show that the stock index has the unit root and exhibit interminable long memory respectively with d=1.245 which is in the interval of 1<d<2. Applying differencing, results show the fractional unit differencing methods eliminates the unwanted interminable long memory better than the first differencing. Furthermore, several ARIMA and ARFURIMA models were identified and estimated. Results indicate ARFURIMA is the best model in terms of fit, serial correlation analysis and accuracy measures. The in-sample forecasts show the adequacy of the ARFURIMA models. Consequently, the out-sample forecasts result show decreasing stock prices indicating that the ARFURIMA is the appropriate model for modelling and forecasting the monthly N30SPI data. This is because the forecast decreasing trend captured by the ARFURIMA model indicate the difficult situation currently witnessed in the Nigerian economy and other economies due to Corona Virus 2019 (COVID-19) pandemic impact. Finally, it is recommended that when the time series is known to have d, in the interval of 1><d<2 applying fractional unit root differencing and estimating ARFURIMA model is appropriate. It helps in achieving reliable forecasts for making future inform-decision. Keywords: Interminable long memory, GPH test, Fractional unit root differencing, ARFURIMA model and monthly stock price index.>. Applying differencing, results show the fractional unit differencing methods eliminates the unwanted interminable long memory better than the first differencing. Furthermore, several ARIMA and ARFURIMA models were identified and estimated. Results indicate ARFURIMA is the best model in terms of fit, serial correlation analysis and accuracy measures. The in-sample forecasts show the adequacy of the ARFURIMA models. Consequently, the out-sample forecasts result show decreasing stock prices indicating that the ARFURIMA is the appropriate model for modelling and forecasting the monthly N30SPI data. This is because the forecast decreasing trend captured by the ARFURIMA model indicate the difficult situation currently witnessed in the Nigerian economy and other economies due to Corona Virus 2019 (COVID-19) pandemic impact. Finally, it is recommended that when the time series is known to have d, in the interval of 1<d<2 applying fractional unit root differencing and estimating ARFURIMA model is appropriate. It helps in achieving reliable forecasts for making future inform-decision. Keywords: Interminable long memory, GPH test, Fractional unit root differencing, ARFURIMA model and monthly stock price index> applying fractional unit root differencing and estimating ARFURIMA model is appropriate. It helps in achieving reliable forecasts for making future inform-decision.