Observation-driven regression models for time series of counts

Mallick, Taslim S. (2004) Observation-driven regression models for time series of counts. Masters thesis, Memorial University of Newfoundland.

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Abstract

There are many situations in practice where one may encounter time series of counts. For example, one may require to analyse a time series of number of tourists or time series of number of patients for a particular disease mainly for the purpose of forecasting of a future count. The analysis of this type of time series of counts is, however, not adequately addressed in the literature. One of the main difficulties in analysing such a time series is the problem of modelling the autocorrelations of the count responses recorded sequentially. In this thesis, we first use an observation-driven correlation model for both stationary and non-stationary Poisson count data. When count responses are subject to overdispersion, one may use a time series of negative binomial counts to analyse such overdispersed and correlated data. There exists a random effects based parameter-driven approach to model this type of time series of negative binomial counts. This approach, however, has some pitfalls as it is difficult to interpret the correlations of observations through the correlations of the random effects. As a remedy, following McKenzie (1986, Adv. Appl. Probab.) we use an observationdriven correlation model to fit correlated negative binomial stationary data. Next we generalize this to the non-stationary data. As far as the estimation of parameters is concerned, we follow Sutradhar (2003, Statistical Science) and use a generalized quasilikelihood approach for the estimation of the associated regression parameter. The overdispersion and correlation parameters are estimated by using the well-known method of moments. This estimation approach yields consistent estimates for all parameters of the model. This consistency property is examined through a simulation study for stationary and non-stationary Poisson as well as negative binomial count data. The estimation method is illustrated by using a real life data that was earlier analyzed by Zeger (1988, Biometrika). We have also developed the formulae for forecasting a future count for the stationary Poisson and negative binomial time series. The performance of the forecasting functions is also examined through a simulation study.

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