Combining Multivariate Volatility Forecasts using Weighted Losses

The ability to improve out-of-sample forecasting performance by combining forecasts is well established in the literature. This paper advances this literature in the area of multivariate volatility forecasts by developing two combination weighting schemes that are capable of placing varying emphasis on losses within the combination estimation period. A comprehensive empirical analysis of the out-of-sample forecast performance across varying dimensions, loss functions, sub-samples and forecast horizons show that new approaches significantly outperform their counterparts in terms of statistical accuracy. Within the financial applications considered, significant benefits from combination forecasts relative to the individual candidate models are observed. Although the more sophisticated combination approaches consistently rank higher relative to the equally weighted approach, their performance is statistically indistinguishable given the relatively low power of these loss functions. Finally, within the applications, further analysis highlights how combination forecasts dramatically reduce the variability in the parameter of interest, namely the portfolio weight or beta.