Comparative Analysis on the Performance of MARFIMA and ARTFIMA in Forecasting the Nigerian All Share Index

Abstract

The Nigeria All Share Index (NASI) is a critical benchmark for the country's stock market performance, exhibiting complex dynamics characterized by nonstationarity, and long range dependence (LRD). Traditional time series models often failed to capture these features adequately. This study conducts a comparative analysis of two advanced fractional integration models Modified Autoregressive Fractionally Integrated Moving Average (MARFIMA) and Autoregressive Tempered Fractionally Integrated Moving Average (ARTFIMA) in modeling and forecasting NASI. The MARFIMA model introduces a sequential differencing filter to address the limitations of classical ARFIMA models, such as slow convergence and truncation errors, while ARTFIMA incorporates tempered fractional differencing to handle heavy-tailed distributions. Using daily NASI data from January 2000 to January 2019, we estimate model parameters via Whittle estimator and evaluate performance using Akaike Information Criterion (AIC), Schwarz Bayesian Information Criterion (SBIC), Root Mean Square Error (RMSE), and Normalized Mean Square Error (NMSE). Results indicate that MARFIMA (2, 1.2, 2) outperforms ARTFIMA (2, -0.4, 2) in model fit (AIC: 53,225.23 vs. 72,046.49) and forecast accuracy (RMSE: 217.155 vs. 435.9115). The superior performance of MARFIMA is attributed to its ability to efficiently remove trends while preserving long memory, making it a robust tool for financial market analysis. These findings have significant implications for investors and policymakers seeking accurate market forecasts in emerging economies.