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Abstract
Integer-valued time series data or count data arise naturally in many areas
including finance, health science , biology, medicine, epidemiology, economics, etc.
Several models and methods for the analysis of time series of count have been developed in recent years. Two broad classes of models used forinteger-valued time series are(i) regression type models and(ii) "thinning" models. In this dissertation, new integer-valued autoregressive(INAR) models are introduced and studied. A typical INAR model can be represented as a sum of two random processes:
Count at time t =Number of survivals at time(t -1)+Increment at time t. The number of survivals depends on the probability of survival, say f. In the current literature the probability of survival f is treated as a fixed parameter and it is assumed to be independent of time t. In many real data sets it may be affected by various environmental factors or others. Hence, f may vary randomly over time. It is therefore useful to develop INAR models for which the survival probability {ft}is a random sequence varying overtime.Wepropose such a random coefficient INAR model and study its properties. For the new models, stationarity and ergodicity properties are established. Conditional least squares, modified quasilikelihood and generalized method of moments are used to estimate the model parameters. Maximum likelihood method is used as a benchmark. Asymptotic properties of the estimates are derived. Simulation results on the comparison of the three estimates are reported. The models are applied to two real data sets.