Forecasting Efficacy of Hybrid ARFIMA-FIGARCH Model: An Application to Returns and Volatility of the Nigerian All Share Index

Abstract

This study investigates the forecasting efficacy of a hybrid AFIMA-FIGARCH model within a fractional integration framework for capturing dual long-memory dynamics: persistence in both returns (conditional mean) and volatility (conditional variance) of the Nigerian All Share Index (ASI) using daily data spanning from January 30th, 2012, to February 7th, 2024 (in 3,138 observations). Initial diagnostics confirmed significant heteroskedasticity (ARCH LM test, p < 0.05) and non-stationarity at levels, justifying the use of volatility-oriented and fractional differencing approaches. Empirical findings reveal extreme persistence characterized by a Hurst exponent (H≈1.13) and an ARFIMA fractional differencing parameter approaching unity (d ≈ 0.999), indicating hyper-persistent dynamics that substantially exceed typical long-memory estimates (d = 0–0.4) reported in African and global financial markets. The ARFRIMA-FIGARCH model demonstrates superior forecasting performance relative to standalone ARFRIMA-GARCH and FIGARCH alternatives, exhibiting curvilinear mean forecasts that reflect mean-reverting tendencies with escalating uncertainty over longer horizons. Diagnostic tests confirmed the model adequacy and stability, with no residual autocorrelation or heteroskedasticity. The near-unit root fractional parameters provided compelling evidence against weak-form market efficiency, indicating that the ASI exhibited prolonged, hyperbolically decaying impacts. These findings underscore the necessity of hybrid long-memory frameworks for risk management, portfolio allocation, and regulatory policy in Nigeria’s emerging financial market.