Risk Forecasting with GARCH, Skewed t Distributions, and Multiple Timescales

Alec N. Kercheval, Yang Liu

Historical time series of asset returns are commonly used to derive forecasts of risk, such as value at risk (VaR). Provided there is enough data, this can be done successfully even though asset returns are typically heavy-tailed, heteroskedastic, and serially dependent. We descri be how the historical data can first be GARCH filtered and then used to calibrate parameters of the heavy-tailed skewed t distribution. Sufficient recent data is available if the forecasting horizon is short enough, for example for daily VaR forecasts. When the horizon is weekly or monthly, howeve r, a sufficiently long weekly or monthly returns series extends too far into the past to be practical.

To address this we introduce a multiple timescale approach, where risk forecas ts at a longer timescale, such as weekly or monthly, can be made with the more abundant data available at a shorter timescale, such as daily or weekly. The method is analyzed both theoretically and empirically using the last few decades of daily S&P500 returns. Since this method is not tied to a particular timescale, it can be used as well for intraday dat a; we illustrate with a set of 1-minute bond index futures returns.

The advantages of this multiscale approach are that it is more adaptable to longer horizons, it increases the quality of forecasts by virtue of increasing the number of recent observations that can be used, and it makes risk forecasts more quickly reactive to recent events that occur late in the most recent period.