FORECASTING THE TAIL DENSITY OF NIGERIAN EXCHANGE RATES WITH A MIXTURE, AUTOREGRESSIVE MODEL

Abstract

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 foreign exchange rates using MAR models with Student-t innovations. The model parameters were estimated using the maximum likelihood method. The forecast results of the MAR model were compared with some competing asymmetric Generalised Autoregressive Conditional Heteroskedastic (GARCH) models. Comparisons were based on the Berkowitz tail test. The test results suggested 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.