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Characterizing heteroskedasticity

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  • Gilles Zumbach

Abstract

Volatility clustering, or heteroskedasticity, is an important feature of all financial time series. In particular, the lagged correlation for the volatility is slowly decreasing with increasing lags. This paper characterizes its decay. First, Monte Carlo simulations are used to select the best volatility and correlation estimators for this task. Second, the empirical lagged correlations are studied over a set of 225 daily time series, and for the DJIA with a sample size of one century. The results strongly favor a log-decay shape, while an exponential and power law decay do not describe the data well. The implications for the description of financial time series by processes are important, as these findings exclude hyperbolic decay, but favor volatility cascade and multi-component ARCH processes. Third, the analysis of the decay coefficient shows that time series related to emerging countries have a shorter memory, in agreement with an analysis of the Hurst exponents published recently.

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  • Gilles Zumbach, 2011. "Characterizing heteroskedasticity," Quantitative Finance, Taylor & Francis Journals, vol. 11(9), pages 1357-1369, October.
    • Handle: RePEc:taf:quantf:v:11:y:2011:i:9:p:1357-1369
    DOI: 10.1080/14697688.2010.535555
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    1. Zumbach, Gilles, 2012. "Option pricing and ARCH processes," Finance Research Letters, Elsevier, vol. 9(3), pages 144-156.
    2. Gilles Zumbach & Luis Fernández, 2012. "Fast and realistic European ARCH option pricing and hedging," Quantitative Finance, Taylor & Francis Journals, vol. 13(5), pages 713-728, November.

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