Parametric methods for time series discrimination

In this thesis we consider the problem of determining whether two or more independent time series have been generated by the same underlying stochastic process, or by the same mechanism.There is an extensive literature on comparing time series from univariate stationary processes on the basis of their second order properties, that is, their dependence structures over time. These existing methods are nonparametric and are based on comparing periodograms or sample autocovariances. They are generally limited by requiring equal sample sizes and Gaussian assumptions. We introduce a parametric approach which involves fitting parametric models to the time series and comparing model parameters. The parametric approach avoids the limitations of the nonparametric and simulations are used to show that it results in a more powerful test. We also show how to extend the parametric approach to compare time series from multivariate stationary processes. A further extension is to compare time series which are from stochastic processes which contain periodic components. Such time series are typically modelled using mixed models which are made up of a deterministic periodic component and a stationary stochastic component. We develop tests for whether two or more time series have been generated by processes with periodicities at the same fixed frequencies and stationary components with the same second order properties. In order to extend the procedures to the multivariate case we first develop novel methods for frequency estimation in the multivariate mixed model.