Mathematics and Physics Seminar Series

AnnouncingAnnouncing

A Seminar Presentation

on Tuesday

February 6, 2018

from 3:00 pm - 3:45 pm in

Maxcy 203

at The University of New Haven

Models for Stationary Count Time Series

— Yisu Jia

PhD Candidate

Department of Mathematical Sciences

Clemson University

Abstract: There has been growing interest in modeling stationary series that have

discrete marginal distributions. Count series arise when describing storm numbers, acci-

dents, wins by a sports team, disease cases, etc. Superpositioning methods have proven

useful in devising stationary count time series having Poisson and binomial marginal distri-

butions. Here, properties of this model class are established and the basic idea is developed.

Speciﬁcally, we show how to construct stationary series with binomial, Poisson, and negative

binomial marginal distributions; other marginal distributions are possible.

A second model for stationary count time series is then proposed. The model uses a la-

tent Gaussian sequence and a distributional transformation to build stationary series with the

desired marginal distribution. The autocovariance functions of the count series are derived

using a Hermite polynomial expansion. This model has proven to be quite ﬂexible. It can

have virtually any marginal distribution, including generalized Poisson and Conway-Maxwell.

As an application, we also study trends in the presence/absence of snow cover (not depths)

in Napoleon, North Dakota from 1966-2015 via satellite data. Statistically, a two-state Markov

chain model with periodic dynamics is developed to describe snow cover presence and its

changes. The results indicate increasing snow coverage in Napoleon, North Dakota

Fur ther Information

For further information, please contact Dr. Yasanthi Kottegoda at the Department of Mathematics and Physics,

Ofﬁce: Maxcy 315, 203-932-1206, YKottegoda@newhaven.edu.