Application of forecast combination in volatility modelling

Abstract

It is well known in the forecasting literature that combining forecasts from different models can often lead to superior forecast performance, at least in the Mean Squares Error (MSE) sense. It has also been noted that combining forecasts by simple averaging often performs better than more sophisticated weighting schemes, although simple averages tend to ignore correlations between forecast errors. However, it is unclear whether these stylized facts hold under different forecast criteria. This is particularly important when evaluating the performance of Value-at-Risk forecasts where MSE is not an appropriate measure. In practice the VaR performance is measured against the Back-testing procedure as outlined in Basel Accord. Given the role of VaR in risk management, it would be important to investigate if forecast combination provided any benefit in forecasting VaR. An interesting implication of this study is that, if forecast combination does in fact provide superior VaR forecasts over individual models, then it also provides a convenience way to combine qualitative forecasts (from expert opinion) and quantitative forecasts (from quantitative models). The combination of qualitative and quantitative forecasts may in fact, enhance the forecast accuracy of VaR further. The aim of this paper is to provide an empirical evaluation of forecast combination for Value-at-Risk. Value-at-Risk forecasts based on four different volatility models, namely, EGARCH, IGARCH, Stochastic Volatility, will be constructed and combined. The forecast performance of the combined forecasts will be compared to the forecast performances of each of the individual models. Two weighting schemes are being considered in this paper, namely, simple weighted average and Quantile Regression (QR). The empirical performances of these forecasts will be based on the percentages of violation as proposed in the Basel Accord with two sets of daily data, namely FTSE and S&P 500, for the period 3 January 1996 to 3 August 2010. The results show that, overall, (i) forecast combination performed better than individual models and (ii) simple weighted average performed better than QR. These results are consistent with the stylised findings in the forecast combination literature. Thus, the paper provided empirical evidence supporting the use of forecast combination in forecasting VaR thresholds.