Modelling time series when mean and variability both change

  • Authors:

  • C. S. Withers;D. P. Krouse;C. P. Pearson;S. Nadarajah

  • Affiliations:

  • Applied Mathematics Group, Industrial Research Limited, Lower Hutt, New Zealand;Applied Mathematics Group, Industrial Research Limited, Lower Hutt, New Zealand;National Institute of Water and Atmospheric Research, Christchurch, New Zealand;School of Mathematics, University of Manchester, Manchester M60 1QD, UK

  • Venue:
  • Mathematics and Computers in Simulation
  • Year:
  • 2008

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Abstract

An extended least-squares method is described which allows us to model the location and scale of a process parametrically without specifying any parametric form for the distribution of the errors. The degree of the associated polynomials is chosen using a step-down method on a table of p-values. A pseudo-likelihood ratio test is given. The concepts of upper and lower return levels are extended to non-stationary series. The method is applied to annual means and extremes of Auckland temperatures. Evidence is found that the mean is changing non-linearly and the variance is also changing for all three series.