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TitleModelling time series when mean and variability both change
Publication TypeJournal Article
Year of Publication2008
AuthorsWithers, C.S., Krouse D.P., Pearson C.P., and Nadarajah S.
JournalMathematics and Computers in Simulation
Pagination57 - 63
Date Published2008
ISSN03784754 (ISSN)
KeywordsChanging variability, Error analysis, Least squares approximations, Likelihood ratio test, MATHEMATICAL MODELS, Non-stationary series, Nonlinear analysis, Parameter estimation, Polynomials, time series analysis, Trends
AbstractAn 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. © 2007 IMACS.

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