EXPLORING THE INAR MODEL ON HEAVY TAILED TIME SERIES DATA WITH OUTLIERS

Abstract

Count data are intrinsically measures of event frequency; it is clear that there is an intrinsic relationship with recurring time to event. Events are typically tallied within time intervals for practical and convenient reasons. The existence of outliers is one issue that prevents count data from being stationary in time series analysis; this has an impact on the effectiveness of fitting several common stationary models to the count data collected over time. Thus, the purpose of this study was to examine how well the Integer Valued Autoregressive (INAR) model performed while modeling count data that included outliers. While this model has been studied for count time series data, it has not been studied for varying degrees of outliers. A monte-carlo simulation was carried out to select the best INAR(p), where p=1,2,3 and 4 on data with 10%, 20% and 30% outliers at different sample sizes. The INAR (4) has the best fit across the sample sizes at the larger percentages of outliers while INAR (3) at the lowest percentage with smallest information criteria of assessment and they are therefore recommended for such modeling.