A Stochastic Volatility Model with Random Level Shifts: Theory and Applications to S&P 500 and NASDAQ Return Indices

51 Pages Posted: 25 Jun 2008

See all articles by Zhongjun Qu

Zhongjun Qu

Boston University

Pierre Perron

Boston University - Department of Economics

Date Written: June 10, 2008

Abstract

Empirical findings 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 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 fit 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 half-life of a typical shock from the short-memory component is very short, on average between 8 and 14 days. We also show that, unlike common stationary short or long-memory models, our model is able to replicate keys features of the data. For the NASDAQ series, it forecasts better than a standard stochastic volatility model, and for the S&P 500 index, it performs equally well.

Keywords: Bayesian estimation, Structural change, Forecasting, Long-memory, State-space models, Latent process

JEL Classification: C11, C12, C53, G12

Suggested Citation

Qu, Zhongjun and Perron, Pierre, A Stochastic Volatility Model with Random Level Shifts: Theory and Applications to S&P 500 and NASDAQ Return Indices (June 10, 2008). Available at SSRN: https://ssrn.com/abstract=1148402 or http://dx.doi.org/10.2139/ssrn.1148402

Zhongjun Qu (Contact Author)

Boston University ( email )

595 Commonwealth Avenue
Boston, MA 02215
United States

Pierre Perron

Boston University - Department of Economics ( email )

270 Bay State Road
Boston, MA 02215
United States
617-353-3026 (Phone)

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