Page 252 - Contributed Paper Session (CPS) - Volume 1

CPS1304 Manik A.

Modeling seasonal epidemic data using integer
autoregressive model
Manik Awale
Savitribai Phule Pune University, Pune, India

Abstract
In this paper we attempt to model the epidemic data using a seasonal integer
valued autoregressive time series model. A seasonal stationary model is
proposed for modeling such data. Various probabilistic and inferential
properties of the model are studied. Simulation studies are carried out to see
the performance of the parameter estimators and to study the forecasting
performance of the model. The model is illustrated with a real data set.

Keywords
Autoregression;Binomial thinning; Coherent forecasting; Surveillance data;
Public health.

1. Introduction
Most of the epidemic surveillance data are counts data and hence
researchers uses the integer-valued autoregressive time series models for the
modeling such type of data. Public health officials collect daily, weekly or
monthly data on number of cases of a various diseases. Here, we consider a
stationary seasonal model based on binomial thinning operator for epidemic
time series data, which is similar to the one introduced by Bourguignon et al.
(2016), but with geometric marginal distributions. In seasonal stationary
models, current value is regressed on the last sth observation − , where

‘s’ is the seasonal period. All the calculations have been performed using R
language for statistical computing (URL: http://www.R-project.org/).

2. Seasonal geometric INAR(1) model based on binomial thinning

The integer-valued auto-regressive process of order one with geometric
marginal distribution and seasonal period ‘s’, (GINAR(1)s) is defined as,
= ∘ − + , ≥ , (1)

where, ‘ ∘ ’ is a binomial thinning operator, ∘ = ∑ are i.i.d. as

,
=0
P(Wi = 0) = 1 − = 1 − P(Wi = 1), ∈ (0,1).

Here, Zt = Ut Mt, ∀ t, with Ut independent of Mt,
P[Ut = 0] = = 1 − P[Ut = 1],

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