Date of Award

12-2009

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Mathematical Science

Advisor

Lund, Robert B.

Committee Member

Kiessler , Peter C.

Committee Member

Gallagher , Colin M.

Committee Member

Brannan , James R.

Abstract

Climatological studies have often neglected changepoint effects when modeling
various physical phenomena. Here, changepoints are plausible whenever a station location moves or its instruments are changed. There is frequently meta-data to
perform sound statistical inferences that account for changepoint
information. This dissertation focuses on two such problems in changepoint analysis.
The first problem we investigate involves assessing trends
in daily snow depth series. Here, we introduce a stochastic storage model. The model allows for seasonal features, which permits the
analysis of daily data. Changepoint times are shown to greatly influence estimated trends in one snow depth series and are accounted for in this analysis. The model is fitted by numerically minimizing a sum of squares of daily prediction errors. Standard errors for the model parameters, useful in making trend inferences, are presented. The methods are illustrated in the analysis of a century of daily snow depth observations from Napoleon, North Dakota.
The results here show that snow depths are significantly declining at Napoleon, with spring ablation occurring earlier, and that changepoint features are very influential in deriving realistic trend estimates.
The second problem considers the asymptotic statistical properties of parameters in a general linear model
experiencing infinitely many level shifts occurring at known times. It is felt that
this setting is more realistic than standard infill asymptotics, where the number of data points between all
changepoint times converges to infinity. Here, least squares estimators
for $m$ trend parameters are derived, and consistency is proven in the case of a short-memory time series
error process.

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