A Stochastic Volatility Model with Random Regime Shifts and its Application to

Abstract Empirical …ndings related to the time series properties of stock returns volatility indicate autocorrelations that decay slowly at long lags. In light of this, several long-memory models have been proposed. However, the possibility of level (regime) shifts has been advanced as a possible explanation for the appearance of long-memory and there is growing evidence suggesting that it may be an important feature of stock returns volatility. Nevertheless, it remains a conjecture that a model incorporating random level shifts in variance can explain the data well and produce reasonable forecasts. We show that a very simple stochastic volatility model incorporating both a random level shift and a short-memory component indeed provides a better in-sample …t of the data and produces forecasts that are no worse, and sometimes better, than standard stationary short and long-memory models. We use a Bayesian method for inference and develop algorithms to obtain the posterior distributions of the parameters and the smoothed estimates of the two latent components. We apply the model to daily S&P 500 and NASDAQ returns over the period 1980.1-2005.12. Although the occurrence of a level shift is rare, about once every two years, the level shift component clearly contributes most to the total variation in the volatility process. The level shifts are also closely linked to the business cycle ‡uctuations. The half-life of a typical shock from the short-memory component is very short, on average between 8 and 14 days. For the NASDAQ series, it forecasts better than a standard stochastic volatility model, and for the S&P 500 index, it performs equally well