Dissertations

5-1-2022

Degree Name

Doctor of Philosophy

Mathematics

Olive, David

Abstract

Inference after model selection is a very important problem. This paper derives the asymptotic distribution of some model selection estimators for autoregressive moving average (ARMA) time series models. Under strong regularity conditions, the model selection estimators are asymptotically normal, but generally the asymptotic distribution is a nonnormal mixture distribution. Hence bootstrap confidence regions that can handle this complicated distribution were used for hypothesis testing. A bootstrap technique to eliminate selection bias is to fit the model selection estimator $\hat{\bbeta}_{MS}^*$ to a bootstrap sample to find a submodel, then draw another bootstrap sample and fit the same submodel to get the bootstrap estimator $\hat{\bbeta}_{MIX}^*$. Prediction intervals for a wide variety of time series models are given, including prediction intervals after model selection.

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