Forecasting daily conditional volatility and h-step-ahead short and long Value-at-Risk accuracy: Evidence from financial data

Abstract

In this article we evaluate the daily conditional volatility and h-step-ahead Value at Risk (VaR) forecasting power of three long memory GARCH-type models (FIGARCH, HYGARCH & FIAPARCH). The forecasting exercise is done for financial assets including seven stock indices (Dow Jones, Nasdaq100, S&P 500, DAX30, CAC40, FTSE100 and Nikkei 225) and three exchange rates vis-a-vis the US dollar (the GBP- USD, YEN-USD and Euro-USD). Because all return series are skewed and fat tailed, each conditional volatility model is estimated under a skewed Student distribution. Consistent with the idea that the accuracy of VaR estimates are sensitive to the adequacy of the volatility model used, h-step-ahead VaR forecasts are based on the skewed Student-t AR(1)-FIAPARCH (1,d,1). This model can jointly accounts for the salient features of financial time series. Our findings reveal that the skewed Student AR (1) FIAPARCH (1.d.1) relatively outperforms the other models in out-of-sample forecasts for one, five and fifteen day forecast horizons. However, there is no difference for the AR (1) FIGARCH (1.d.1) and AR (1) HYGARCH (1.d.1) models since they have the same forecasting ability. Results indicate also that skewed Student-t FIAPARCH (1,d,1) model provides more accurate one-day-ahead VaR forecasts for both long and short trading positions than those generated using alternative horizons (5-day and 15-day-ahead). This result holds for each of the financial time series.