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The Variance of Sample Autocorrelations: Does Barlett's Formula Work With ARCH Data?

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  • Kokoszka, Piotr S.
  • Politis, D N
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    Abstract

    We review the notion of linearity of time series, and show that ARCH or stochastic volatility (SV) processes are not only non-linear: they are not even weakly linear, i.e., they do not even possess a martingale representation. Consequently, the use of Bartlett’s formula is unwarranted in the context of data typically modelled as ARCH or SV processes such as financial returns. More surprisingly, we show that even the squares of an ARCH or SV process are not weakly linear. Finally, we present an alternative to Bartlett’s formula that is applicable (and consistent) in the context of financial returns data.

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    Bibliographic Info

    Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt68c247dp.

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    Date of creation: 09 Oct 2008
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    Handle: RePEc:cdl:ucsdec:qt68c247dp

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    Keywords: ARCH; stochastic volatility; time series;

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    1. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(01), pages 3-22, February.
    2. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
    3. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    4. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
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