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Processes for stocks capturing their statistical properties from one day to one year

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  • Gilles Zumbach
  • Luis Fern�ndez
  • Caroline Weber

Abstract

A realistic ARCH process is set up so as to duplicate, for all practical purposes, the properties of stock time series from 1 day to 1 year. The process includes heteroskedasticity with long memory, leverage, fat-tail innovations, relative return, price granularity, and holidays. Its adequacy to describe empirical data is controlled over a broad panel of statistics, including (robust L-statistics) skew, (robust) kurtosis, shape factor for the volatility distribution, and lagged correlations between combinations of return and volatility. These statistics are computed for returns and volatilities with characteristic time intervals ranging from 1 day to 1 year. This wide cross-check between stock time series and simulations ensures that the most important features of the data are correctly captured by the process up to 1 year. The by-products of the statistical analyses and estimations are (1) a positive skew, (2) a cross-sectional relation between kurtosis and heteroskedasticity, (3) a very similar cross-sectional distribution for the statistics evaluated over the empirical data set or for the process with one set of parameters and (4) the heteroskedasticity is very close to an integrated volatility process.

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  • Gilles Zumbach & Luis Fern�ndez & Caroline Weber, 2014. "Processes for stocks capturing their statistical properties from one day to one year," Quantitative Finance, Taylor & Francis Journals, vol. 14(5), pages 849-861, May.
    • Handle: RePEc:taf:quantf:v:14:y:2014:i:5:p:849-861
    DOI: 10.1080/14697688.2013.765956
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    References listed on IDEAS

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    1. Wiesław Dębski & Ewa Feder-Sempach & Szymon Wójcik, 2018. "Statistical Properties of Rates of Return on Shares Listed on the German, French, and Polish Markets – a Comparative Study," Contemporary Economics, University of Economics and Human Sciences in Warsaw., vol. 12(1), March.

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