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) to 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; and (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 different series, and compare its forecasting performance with those of a variety of competing models at various horizons. A striking feature is that the modified RLS model has the smallest mean square forecast errors in 64 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 modified RLS model offers important gains in forecasting performance.