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Vol 6, No 2 :

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A Seasonal INAR(1) Process with Geometric Innovation for Over dispersed Count Time Series
E W Okereke , S. N. Gideon , C O Omekara
Abstract

A seasonal integer valued autoregressive model of first order with geometric innovation INARG(1)s was proposed in this study. The autocorrelation function (ACF), the marginal mean and the marginal variance of the model were obtained. The Yule-Walker (YW) estimators and conditional least squares (CLS) estimators of the parameters of the model were derived. The CLS estimators were shown to be asymptotically normal. The minimum mean square error (MMSE) forecast function was derived based on the proposed model. The forecast function was found to be equal to the conditional expectation of given  (L-step ahead forecast given the last observation on the given series). A simulation study was carried out to compare YW and CLS estimates and forecasting performance of INARG(1)12 model and the non-seasonal INARG(1) model. A set of real data was analysed and forecast evaluation criteria were obtained. The forecasting performance of INARG(1)12 model was compared with that of each of the INARG(1) model, the Gaussian SARIMA(0,0,0) (1,0,0)12 model and the seasonal geometric integer-valued autoregressive process based on negative binomial thinning (SGINAR(12) model). Our empirical results revealed that the INARG(1)12model can be a better model for modelling over dispersed stationary seasonal count time series, when the series is generated from a Bernoulli process, than each of  the INARG(1) model, Gaussian SARIMA(0,0,0) (1,0,0)12 model and  SGINAR(12) model.
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ISSN(P) 2350-0174

ISSN(O) 2456-2378

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