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

*Zhongjun Qu* () and
*Pierre Perron* ()

No wp2008-007, Boston University - Department of Economics - Working Papers Series from Boston University - Department of Economics

**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 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 (search for similar items in EconPapers)

**JEL-codes:** C11 C12 C53 G12 (search for similar items in EconPapers)

**New Economics Papers:** this item is included in nep-ecm, nep-ets, nep-fmk, nep-for and nep-ore

**Date:** 2008-06

**References:** View references in EconPapers View complete reference list from CitEc

**Citations:** View citations in EconPapers (1) Track citations by RSS feed

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:bos:wpaper:wp2008-007

Access Statistics for this paper

More papers in Boston University - Department of Economics - Working Papers Series from Boston University - Department of Economics Contact information at EDIRC.

Bibliographic data for series maintained by Program Coordinator ().