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

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  • Ana Pérez
  • Esther Ruiz

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. , .

Suggested Citation

  • Ana Pérez & Esther Ruiz, 2003. "Properties of the Sample Autocorrelations of Nonlinear Transformations in Long-Memory Stochastic Volatility Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(3), pages 420-444.
  • Handle: RePEc:oup:jfinec:v:1:y:2003:i:3:p:420-444
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    Cited by:

    1. Broto, Carmen & Ruiz, Esther, 2006. "Unobserved component models with asymmetric conditional variances," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2146-2166, May.
    2. Ruiz, Esther & Veiga, Helena, 2008. "Modelling long-memory volatilities with leverage effect: A-LMSV versus FIEGARCH," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2846-2862, February.
    3. Dalla, Violetta, 2015. "Power transformations of absolute returns and long memory estimation," Journal of Empirical Finance, Elsevier, vol. 33(C), pages 1-18.
    4. Marian Vavra, 2012. "Testing Non-linearity Using a Modified Q Test," Birkbeck Working Papers in Economics and Finance 1204, Birkbeck, Department of Economics, Mathematics & Statistics.
    5. Ruiz Esther & Pérez Ana, 2012. "Maximally Autocorrelated Power Transformations: A Closer Look at the Properties of Stochastic Volatility Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(3), pages 1-33, September.
    6. Veiga, Helena, 2006. "A two factor long memory stochastic volatility model," DES - Working Papers. Statistics and Econometrics. WS ws061303, Universidad Carlos III de Madrid. Departamento de Estadística.

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