Forecasting the Tail Density of Nigerian Exchange Rates from a Mixture Autoregressive model

Forecasts play a very significant role in economics, finance and other fields of application of time series analysis. Density forecasts have become more popular as real life scenarios require not only a forecast estimate but also the uncertainty associated with such a forecast. The class of mixture autoregressive (MAR) models provide a flexible way to model various features of financial time series and are also suitable for density forecasting. This study forecasted the out-of-sample tail density of Nigerian exchange rates using MAR models with Student-t innovations. The model parameters were estimated using the maximum likelihood method. The forecast results were compared with some competing asymmetric GARCH models. Comparisons were based on the Berkowitz tail test. The test results report that the MAR model provided the best out-of-sample tail-density forecasts. The findings support the suggestion that the MAR models are well suited to capture the kind of data dynamics present in financial data and provide a useful alternative to other models