Mathematics and Physics Seminar Series
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,