New goodness-of-fit tests for the error distribution of autoregressive time-series models

  • Authors:

  • C. J. Swanepoel;W. O. Doku

  • Affiliations:

  • Department of Statistics, Potchefstroom University for CHE, 2520 Potchefstroom, South Africa;Department of Statistics, Potchefstroom University for CHE, 2520 Potchefstroom, South Africa

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2003

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Abstract

New goodness-of-fit tests, based on bootstrap estimated expectations of probability integral transformed order statistics, are derived for the error distribution of autoregressive time-series models. The resulting test statistics are location and scale invariant, and are sensitive to discrepancies at the tails of the hypothesised distribution. It is shown how critical points for all sample sizes and significance levels can be obtained by using the parametric bootstrap. A simulation study shows that one of the new proposed tests is more powerful than the established Shapiro-Wilk test and the well-known score test (also known as the Lagrange multiplier test), for a wide range of alternative distributions and sample sizes.