A novel hybrid ARFURIMA-APARCH model for modeling interminable long memory and asymmetric effect in time series

Abstract

In this paper, we introduce a new hybrid model namely Autoregressive Fractional Unit Root Integrated Moving Average-Asymmetric Power Autoregressive Conditional Heteroscedasticity (ARFURIMA-APARCH) model. The Nigeria daily COVID19 records and Bitcoin to EURO exchange rate that exhibit a type of Long Memory (LM) called Interminable LM (ILM), volatility and asymmetric (leverage) effect were used to show the applications of the proposed ARFURIMA-APARCH model. The existing Autoregressive Fractional Integrated Moving Average-Asymmetric Power Autoregressive Conditional Heteroscedasticity (ARFIMA-APARCH) model were estimated and compared with the ARFURIMA-APARCH model. Results showed that the new hybrid model is better based on goodness-of-fit, serial correlation tests and forecast measures of accuracy. As a conclusion, our study showed that the ARFURIMA-APARCH model performed better compared to the ARFIMA-APARCH hybrid model. Therefore, the ARFURIMA-APARCH model is a better option for modeling ILM, volatility and leverage effect of health and financial data. Future study should focus on the application of the developed hybrid ARFURIMA-APARCH model using some major economic indicators, for example, Gross Domestic Product (GDP), currency exchange rate, stock price index, interest rate and other financial data.