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Home  >  Volume 38

22. On the Performance of Mixture Autoregressive Model in Modelling Naira-Dollar Exchange Rates by J.F. Ojo and R.O. Olanrewaju Volume 38, pp 155 – 166
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Abstract

Linear time series models such as Auto-Regressive (AR), Auto-Regressive Moving Average (ARMA) and Auto-Regressive Integrated Moving Average (ARIMA) have been widely used to model Naira-Dollar exchange rates. Also, non-linear models such as Generalized Autoregressive Conditional Heteroscedasticity (GARCH) and Self-Exciting Threshold Auto-Regressive (SETAR) have been frequently used to model Naira-Dollar exchange rates. These non-linear models could only capture bi-modal and two regime-switching in a financial time series. This study attempts to model Naira-Dollar exchange rates using Mixture Auto-Regressive (MAR) model since less attention has been given to MAR in modelling Naira-Dollar exchange rates. Unlike GARCH and SETAR and other linear models, MAR model could capture multi-modalities that is more than two regime-switching including their volatilities. The Naira-Dollar exchange rates between 1:2004 and 12:2014 was fitted to MAR model because of its regime-switching stylized attributes and compared with AR, GARCH, and SETAR. The Normal-QQ plot and the density function plot of the Naira-Dollar exchange rates between 1:2004 and 12: 2014 revealed a 5-regime-shift.  In addition, the multi-modal distributions of the first and last two regimes are leptokurtic while the second and third regimes are mesokurtic in nature. An AR (1), GARCH (1, 1), SETAR (2:1, 4) and MAR (5:2, 1, 1, 1, 1) models were best fitted to the Naira-Dollar exchange rates using appropriate estimation techniques and their Akaike Information Criteria(AIC) and log-likelihoodwere given as (467.4)(-232.70), (465.9)(-235.84), (425.35)(-241.68) and (401.23)(-287.08), respectively. In terms of model performance, it was observed that the MAR model has the minimum AIC and log-likelihood of 401.23 and (-287.08), respectively. Also, the conditional variances (volatilities) of the five regimes were 0.5544, 3.1206, 4.9783, 0.5546 and 15.9736. It was noted that the last regime which was around 2012 and 2014 recorded the highest volatility. Furthermore, the predictive distribution power ofMAR made it preferable to the compared models as its predictions were very close to actual monthly Naira-Dollar exchange rates for 1:12, 2015that was purposely left out for comparison.

Keywords: Mixture Auto-Regressive, Multimodalities, Naira-Dollar exchange rates, Regime-switching

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