Assessing the Performance of the MARFIMA Model Using Simulated and Real Life Data

Abstract

A modified autoregressive fractional integrated moving average MARFIMA (p, d, q) is presented in this study to describe time series data that are nonstationary and have a fractional difference value of 1<d<1.5. Data from ARFIMA simulations are used to assess the performance of the MARFIMA model. The autoregressive fractional integrated moving average ARFIMA model and the MARFIMA model's performance were also compared in a number of applications. Using the Akaike Information Criterion (AIC), Schwartz Bayesian Information Criterion (SBIC), root mean square error (RMSE), and normalized mean square error (NMSE), the best model was chosen, and its performance was evaluated using a variety of forecast accuracy metrics. Results indicated that across four distinct financial and economic data sets, which include the price of crude oil, the Nigerian stock market, the Nigerian all-shares index, and the Nigerian food and beverage index, the MARFIMA model performed better than the ARFIMA model. The research provides a more robust method for modeling and forecasting long memory data. The study has also contributed to existing literature on the most appropriate method for modelling long memory associated with financial and economic data.