A First-Order Poisson Random-Coefficient Mixed-Thinning Integer-Valued Autoregressive Model for Analyzing Crime Data from Inverell, NSW

Abstract

To handle data that involve counting elements with variable characteristics, the paper develops a first-order Poisson random coefficient mixed thinning integer-valued autoregressive time series model. Moments and autocovariance functions for this model are studied since the distribution of the innovation sequence is Poisson. Based on these theoretical foundations, the conditional least squares and conditional maximum likelihood methods are employed to estimate the parameters of the model. Asymptotic properties of the obtained estimators are established. The performances of these estimators are evaluated via simulations, and the conclusion is drawn that the conditional maximum likelihood method is superior. Furthermore, a set of crime data from the town of Inverell in New South Wales, Australia, is analyzed to demonstrate the practical relevance of the model.

Keywords

Conditional least squares estimation / Conditional maximum likelihood estimation / Po-RCMTINAR(1) model / Mixed thinning / Asymptotic distribution / NSW Inverell crime data / 62F10 / 62F03

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Funding

National Natural Science Foundation of China(No.11871028, 11731015)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature

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