Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Statistics and Actuarial Sciences

Supervisor

A.I. McLeod

Abstract

In this thesis, a new univariate-multivariate portmanteau test is derived. The proposed test statistic can be used for diagnostic checking ARMA, VAR, FGN, GARCH, and TAR time series models as well as for checking randomness of series and goodness-of- fit VAR models with stable Paretian errors. The asymptotic distribution of the test statistic is derived as well as a chi-square approximation. However, the Monte-Carlo test is recommended unless the series is very long. Extensive simulation experiments demonstrate the usefulness of this test and its improved power performance compared to widely used previous multivariate portmanteau diagnostic check. The contributed R package portes is also introduced. This package can utilize multi-core CPUs often found in modern personal computers as well as a computer cluster or grid. The proposed package includes the most important univariate and multivariate diagnostic portmanteau tests with the new test statistic given in this thesis. It is also useful for simulating univariate/multivariate data from nonseasonal ARIMA/VARIMA process with nite or in nite variances, testing for stationarity and invertibility, and estimating parameters from stable distributions. Many illustrative applications are given. In this thesis, it has been shown that the classical ordinary least squares regression may produce smaller p-values than it should due to the lack of statistical independency in the tted model which may invalidate the statistical inferences. The Poincare plots are suggested to check for such hidden positive correlations.

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