Date of Award
8-2009
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Legacy Department
Mathematical Science
Committee Chair/Advisor
Lund, Robert B
Committee Member
Gallagher , Colin M
Committee Member
Kiessler , Peter C
Committee Member
Kulasekera , Karunarathna B
Abstract
This research proposes a new but simple model for stationary time series of integer counts. Previous work in the area has focused on mixture and thinning methods and links to classical time series autoregressive moving-average difference equations; in contrast, our methods use a renewal process to generate a correlated sequence of Bernoulli trials. By superpositioning independent copies of such processes, stationary series with binomial, Poisson, geometric, or any other discrete marginal distribution can be readily constructed. The model class proposed is parsimonious, non-Markov, and readily generates series with either short or long memory autocovariances. The model can be fitted with linear prediction techniques for stationary series. Estimation of process parameters based on conditional least squares methods is considered. Asymptotic properties of the estimators are derived. The models sometimes have an autoregressive moving-average structure and we consider the AR(1) count process case in detail. Unlike previous methods based on mixture and thinning tactics, series with negative autocorrelations can be produced.
Recommended Citation
Cui, Yunwei, "Integer-valued time series and renewal processes" (2009). All Dissertations. 401.
https://tigerprints.clemson.edu/all_dissertations/401