Properties of the Sample Autocorrelations of Nonlinear Transformations in Long-Memory Stochastic Volatility Models

Posted: 29 Feb 2008

See all articles by Ana Pérez

Ana Pérez

University of Valladolid - Faculty of Law

Esther Ruiz

Charles III University of Madrid - Department of Statistics and Econometrics

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Date Written: 2003

Abstract

The autocorrelations of log-squared, squared, and absolute financial returns are often used to infer the dynamic properties of the underlying volatility. This article shows that, in the context of long-memory stochastic volatility models, these autocorrelations are smaller than the autocorrelations of the log volatility and so is the rate of decay for squared and absolute returns. Furthermore, the corresponding sample autocorrelations could have severe negative biases, making the identification of conditional heteroscedasticity and long memory a difficult task. Finally, we show that the power of some popular tests for homoscedasticity is larger when they are applied to absolute returns.

Keywords: absolute transformation, Box-Ljung text, conditional heteroscedasticity, log-squared transformation, Peña Rodriguez test, squared observations

Suggested Citation

Pérez, Ana and Ruiz, Esther, Properties of the Sample Autocorrelations of Nonlinear Transformations in Long-Memory Stochastic Volatility Models ( 2003). Journal of Financial Econometrics, Vol. 1, pp. 420-444, 2003, Available at SSRN: https://ssrn.com/abstract=892382

Ana Pérez (Contact Author)

University of Valladolid - Faculty of Law

47002 Valladolid
Spain

Esther Ruiz

Charles III University of Madrid - Department of Statistics and Econometrics ( email )

c/ Madrid 126
Getafe (Madrid), 28903
Spain

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