Order identification and estimation of moving average and auto-regressive dynamic models for count time series

Balakrishnan, Kirushanthini (2019) Order identification and estimation of moving average and auto-regressive dynamic models for count time series. Masters thesis, Memorial University of Newfoundland.

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Abstract

Time series of count data occur frequently in practice such as in medical studies and life sciences. Identification of a proper model for time series data is extremely important as it reects the underlying structure of the time series and the fitted model will be used for forecasting. We first discuss the basic properties of the stationary Poisson moving average (MA) and stationary Poisson auto-regressive (AR) processes up to order 3 with the intention of finding a method for model identification. Some authors have derived and discussed the basic properties of stationary Poisson MA(q) process and stationary Poisson AR(1) and AR(2) processes for analysis of count time series data. We have extended to stationary Poisson AR(3) process and derived the basic properties of mean, variance, covariance and correlation of it. We discussed auto-correlation function (ACF) of stationary Poisson MA and AR processes up to order 3 and derived partial auto-correlation function (PACF) of stationary Poisson MA up to order 2 and stationary Poisson AR processes up to order 3 in order to find the theoretical patterns of the processes for model identification purposes. The patterns and behaviour of ACF and PACF of these stationary MA and AR Poisson models have been discussed in detail. In each of the cases, the accuracy of the patterns of ACF and PACF are examined through simulation studies. We found that patterns in the ACF and PACF of these models are similar to those of AR and MA models for Gaussian processes. We have also proposed a model for non stationary Poisson AR(3) process and the basic properties have been derived. Model parameters are estimated using generalized quasi-likelihood (GQL) and generalized method of moment (GMM) methods. The performance of the estimation methods have been examined through simulation studies.

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