Out-of-sample Forecasting Performance of Won/Dollar Exchange Rate Return Volatility Model
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We compare the out-of-sample forecasting performance of volatility models using daily exchange rate for the KRW/USD during the period from 1992 to 2008. For various forecasting horizons, historical volatility models with a long memory tend to make more accurate forecasts. Especially, we carefully observe the difference between the EWMA and the GARCH(1,1) model. Our empirical finding that the GARCH model puts too much weight on recent observations relative to those in the past is consistent with prior evidence showing that asset market volatility has a long memory, such as Ding and Granger (1996). The forecasting model with the lowest MSFE and VaR forecast error among the models we consider is the EWMA model in which the forecast volatility for the coming period is a weighted average of recent squared return with exponentially declining weights. In terms of forecast accuracy, it clearly dominates the widely accepted GARCH and rolling window GARCH models. We also present a multiple comparison of the out-of-sample forecasting performance of volatility using the stationary bootstrap of Politis and Romano (1994). We find that the White's reality check for the GARCH(1,1) expanding window model and the FIGARCH(1,1) expanding window model clearly reject the null hypothesis and there exists a better model than the two benchmark models. On the other hand, when the EWMA model is the benchmark, the White's for all forecasting horizons are very high, which indicates the null hypothesis may not be rejected. The Hansen's report the same results. The GARCH(1,1) expanding window model and the FIGARCH(1,1) expanding window model are dominated by the best competing model in most of the forecasting horizons. In contrast, the RiskMetrics model seems to be the most preferred. We also consider combining the forecasts generated by averaging the six raw forecasts and a trimmed set of forecasts which calculate the mean of the four forecasts after disregarding the highest and lowest forecasts from the six models. This experiment confirms that the forecast combinations always outperform forecasts from a single model.
Abstract
We compare the out-of-sample forecasting performance of volatility models using daily exchange rate for the KRW/USD during the period from 1992 to 2008. For various forecasting horizons, historical volatility models with a long memory tend to make more accurate forecasts. Especially, we carefully observe the difference between the EWMA and the GARCH(1,1) model. Our empirical finding that the GARCH model puts too much weight on recent observations relative to those in the past is consistent with prior evidence showing that asset market volatility has a long memory, such as Ding and Granger (1996). The forecasting model with the lowest MSFE and VaR forecast error among the models we consider is the EWMA model in which the forecast volatility for the coming period is a weighted average of recent squared return with exponentially declining weights. In terms of forecast accuracy, it clearly dominates the widely accepted GARCH and rolling window GARCH models. We also present a multiple comparison of the out-of-sample forecasting performance of volatility using the stationary bootstrap of Politis and Romano (1994). We find that the White's reality check for the GARCH(1,1) expanding window model and the FIGARCH(1,1) expanding window model clearly reject the null hypothesis and there exists a better model than the two benchmark models. On the other hand, when the EWMA model is the benchmark, the White's for all forecasting horizons are very high, which indicates the null hypothesis may not be rejected. The Hansen's report the same results. The GARCH(1,1) expanding window model and the FIGARCH(1,1) expanding window model are dominated by the best competing model in most of the forecasting horizons. In contrast, the RiskMetrics model seems to be the most preferred. We also consider combining the forecasts generated by averaging the six raw forecasts and a trimmed set of forecasts which calculate the mean of the four forecasts after disregarding the highest and lowest forecasts from the six models. This experiment confirms that the forecast combinations always outperform forecasts from a single model.
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