Assessing the Forecast Performance of ARTFIMA-FIAPARCH Hybrid Model

Abstract

The Long Memory (LM) phenomenon denotes a prolonged association between sequentially gathered observations, characterized by a gradual decline in the autocorrelation function. The Autoregressive Tempered Fractional Integrated Moving Average (ARTFIMA) model addresses non-stationary time series displaying LM in the mean. Conversely, the Fractionally Integrated Asymmetric Power Autoregressive Conditional Heteroscedasticity (FIAPARCH) model is tailored for data exhibiting LM in volatility.This study introduces a novel hybrid model, ARTFIMA-FIAPARCH, employing a transformation method to tackle issues of serial correlation and heteroscedasticity identified in the residuals of the ARTFIMA model. This innovative hybrid model is evaluated using both simulated and real-world data, specifically Naira-Dollar exchange rate data. The assessment involves comparing its performance with existing models like ARFIMA, ARTFIMA and ARFIMA-FIAPARCH based on the minimum Akaike Information Criterion (AIC) and forecast accuracy measures (MAE and RMSE). The findings indicate that ARTFIMA (0,1.3,1.03,3)-FIAPARCH (1,0.08,1) emerges as the superior choice within the ARTFIMA-FIAPARCH models, surpassing ARFIMA (3,1.03,0)-FIAPARCH (1,0.08,1). Conclusively, ARTFIMA-FIAPARCH proves to be a favorable model for examining the mean, volatility and leverage effects of any given economic and financial data. However, it is recommended that economists and financial institutions consider adopting ARTFIMAFIAPARCH as a viable alternative to existing models.