Forecasting Return Volatility: Level Shifts with Varying Jump Probability and Mean Reversion

We extend the random level shift (RLS) model of Lu and Perron (2010) for the volatility of asset prices, which consists of a short memory process and a random level shift component. Motivated by empirical features a) we specify a time-varying probability of shifts as a function of large negative lagged returns; b) we incorporate a mean reverting mechanism so that the sign and magnitude of the jump component change according to the deviations of past jumps from their long run mean. This allows the possibility of forecasting the sign and magnitude of the jumps. We estimate the model using twelve di§erent series. We compare its forecasting performance with a variety of competing models at various horizons. A striking feature is that the modiÖed RLS model has the smallest mean square forecast errors in 64 out of the 72 cases, while it is a close second for the other 8 cases. The improvement in forecast accuracy is often substantial, especially for medium to long-horizon forecasts. This is strong evidence that our modiÖed RLS model o§ers important gains in forecasting performance.