THE PERFORMANCE OF INTEGER-VALUED AUTO-REGRESSIVE (INAR) MODEL IN ZERO INFLATED DATA

Abstract

Time series count data frequently exhibits zero inflation and even heavy-tailedness in practical applications. Many models have been proposed for modelling count data, but heavy-tailedness is less considered. The effect of excess zeros on time series count data cannot be disregarded. Thus, there is a need for a model that would cater for excess zeros in the time series data. The proposed model, a new integer-valued autoregressive process, is expected to capable of capturing these features. This study therefore investigates the effectiveness of Integer-Valued Autoregressive (INAR) models in handling time series count data at different proportions of excess zeros, determine the predictive ability of   INAR models at different steps ahead and compare its performance with orders of model {INAR (1), INAR (2), INAR (3) and INAR (4)} being used for the data. The effects of sample sizes on the performance of the models were also studied through simulation. At every sample size, the best status of the orders p, where p = 1, 2, 3, 4 are respectively determined for   20%, 30% and 40% proportions of the excess zeros using information criteria AIC, BIC and HQIC.  Forecast accuracy was assessed using the Thiel’s U statistic, where lower values indicate better performance. INAR (3) achieved the lowest AIC, BIC and HQIC values across most scenarios indicating a strong model fit and is suggested for use in fitting any time series of count to the underlying features given in this dissertation.