Applications of Mathematics, Vol. 63, No. 1, pp. 79-105, 2018
A zero-inflated geometric INAR(1) process with random coefficient
Hassan S. Bakouch, Mehrnaz Mohammadpour, Masumeh Shirozhan
Received March 26, 2017. First published January 25, 2018.
Abstract: Many real-life count data are frequently characterized by overdispersion, excess zeros and autocorrelation. Zero-inflated count time series models can provide a powerful procedure to model this type of data. In this paper, we introduce a new stationary first-order integer-valued autoregressive process with random coefficient and zero-inflated geometric marginal distribution, named ZIGINAR$_{\rm RC}(1)$ process, which contains some sub-models as special cases. Several properties of the process are established. Estimators of the model parameters are obtained and their performance is checked by a small Monte Carlo simulation. Also, the behavior of the inflation parameter of the model is justified. We investigate an application of the process using a real count climate data set with excessive zeros for the number of tornados deaths and illustrate the best performance of the proposed process as compared with a set of competitive INAR(1) models via some goodness-of-fit statistics. Consequently, forecasting for the data is discussed with estimation of the transition probability and expected run length at state zero. Moreover, for the considered data, a test of the random coefficient for the proposed process is investigated.
Keywords: randomized binomial thinning; geometric minima; estimation; likelihood ratio test; mixture distribution; realization with random size
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