Time series exponential models: theory and methods

Abstract

The exponential model of Bloomfield (1973) is becoming increasingly important due to its recent applications to long memory time series. However, this model has received little consideration in the context of short memory time series. Furthermore, there has been very little attempt at using the EXP model as a model to analyze observed time series data. This dissertation research is largely focused on developing new methods to improve the utility and robustness of the EXP model. Specifically, a new nonparametric method of parameter estimation is developed using wavelets. The advantage of this method is that, for many spectra, the resulting parameter estimates are less susceptible to biases associated with methods of parameter estimation based directly on the raw periodogram. Additionally, several methods are developed for the validation of spectral models. These methods test the hypothesis that the estimated model provides a whitening transformation of the spectrum; this is equivalent to the time domain notion of producing a model whose residuals behave like the residuals of white noise. The results of simulation and real data analysis are presented to illustrate these methods.