The Effect of (Mis-Specified) GARCH Filters on the Finite Sample Distribution of the BDS Test

  • Authors:

  • Chris Brooks;Saeed M. Heravi

  • Affiliations:

  • ISMA Centre, Department of Economics, The University of Reading, Whiteknights, Reading RG6 6AA, UK/ e-mail: c.brooks@reading.ac.uk;Cardiff Business School, University of Wales, Cardiff CF1 3AT, UK

  • Venue:
  • Computational Economics
  • Year:
  • 1999

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Abstract

This paper considers the effect of using a GARCH filter on the properties of the BDS test statistic as well as a number of other issues relating to the application of the test. It is found that, for certain values of the user-adjustable parameters, the finite sample distribution of the test is far-removed from asymptotic normality. In particular, when data generated from some completely different model class are filtered through a GARCH model, the frequency of rejection of iid falls, often substantially. The implication of this result is that it might be inappropriate to use non-rejection of iid of the standardised residuals of a GARCH model as evidence that the GARCH model ’fits‘ the data.