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Autoregressive Conditional Heteroskedasticity

In: Introduction to Modern Time Series Analysis

Author

Listed:
  • Gebhard Kirchgässner

    (University of St. Gallen)

  • Jürgen Wolters

    (Freie Universität Berlin)

Abstract

All models discussed so far use the conditional expectation to describe the mean development of one or more time series. The optimal forecast, in the sense that the variance of the forecast errors will be minimised, is given by the conditional mean of the underlying model. Here, it is assumed that the residuals are not only uncorrelated but also homoskedastic, i.e. that the unexplained fluctuations have no dependencies in the second moments. However, Benoit Mandelbrot (1963) already showed that financial market data have more outliers than would be compatible with the (usually assumed) normal distribution and that there are ‘volatility clusters’: small (large) shocks are again followed by small (large) shocks. This may lead to ‘leptokurtic distributions’, which — as compared to a normal distribution — exhibit more mass at the centre and at the tails of the distribution. This results in ‘excess kurtosis’, i.e. the values of the kurtosis are above three.

Suggested Citation

  • Gebhard Kirchgässner & Jürgen Wolters, 2007. "Autoregressive Conditional Heteroskedasticity," Springer Books, in: Introduction to Modern Time Series Analysis, chapter 7, pages 241-265, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-73291-4_7
    DOI: 10.1007/978-3-540-73291-4_7
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