The detection and estimation of long memory in stochastic volatility. (English) Zbl 0905.62116

Breidt, F. Jay; Crato, Nuno; de Lima, Pedro

J. Econom. 83, No. 1-2, 325-348 (1998).

Empirical research suggests that stock market indices can be well-described by long-memory conditional variance models. The authors have found evidence of a long memory in variance proxies using both nonparametric and semiparametric tests and show by simulations that these tests are able to distinguish long and short memory in the volatilies. The long memory stochastic volatility (LMSV) model is constructed by incorporating an ARFIMA process in a standard stochastic volatility scheme and is used for the analysis. Estimators of the parameters of the model are obtained by maximizing the spectral approximation to the Gaussian likelihood and it is shown that these estimators are strongly consistent. Finite-sample Monte-Carlo simulation results show that the above estimators have reasonable properties for series usually available for financial data. An empirical study with a long series of stock prices shows the better performance of the LMSV model over short-memory models.

Reviewer: V.Parkhomenko (Kyïv)

MSC:

62P20	Applications of statistics to economics
91B84	Economic time series analysis
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)

Keywords:

spectral likelihood estimators; long memory stochastic volatility; fractional ARMA; EGARCH

Software:

longmemo

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