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A powerful test for conditional heteroscedasticity for financial time series with highly persistent volatilities


  • Rodríguez, Julio
  • Ruiz, Esther


Traditional tests for conditional heteroscedasticity are based on testing for significant autocorrelations of squared or absolute observations. In the context of high frequency time series of financial returns, these autocorrelations are often positive and very persistent, although their magnitude is usually very small. Moreover, the sample autocorrelations are severely biased towards zero, specially if the volatility is highly persistent. Consequently, the power of the traditional tests is often very low. In this paper, we propose a new test that takes into account not only the magnitude of the sample autocorrelations but also possible patterns among them. This aditional information makes the test more powerful in situations of empirical interest. The asymptotic distribution of the new statistic is derived and its finite sample properties are analized by means of Monte Carlo experiments. The performance of the new test is compared with other alternative tests. Finally, we illustrate the results analysing several real time series of financial returns.

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  • Rodríguez, Julio & Ruiz, Esther, 2003. "A powerful test for conditional heteroscedasticity for financial time series with highly persistent volatilities," DES - Working Papers. Statistics and Econometrics. WS ws036716, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:ws036716

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    References listed on IDEAS

    1. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    2. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    3. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    4. Andersen, Torben G & Bollerslev, Tim, 1997. " Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," Journal of Finance, American Finance Association, vol. 52(3), pages 975-1005, July.
    5. Bollerslev, Tim & Ole Mikkelsen, Hans, 1999. "Long-term equity anticipation securities and stock market volatility dynamics," Journal of Econometrics, Elsevier, vol. 92(1), pages 75-99, September.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
    8. repec:bla:restud:v:65:y:1998:i:3:p:361-93 is not listed on IDEAS
    9. Pena D. & Rodriguez J., 2002. "A Powerful Portmanteau Test of Lack of Fit for Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 601-610, June.
    10. Carnero, María Ángeles & Peña, Daniel & Ruiz, Esther, 2001. "Is stochastic volatility more flexible than garch?," DES - Working Papers. Statistics and Econometrics. WS ws010805, Universidad Carlos III de Madrid. Departamento de Estadística.
    11. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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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.

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