Models for autoregressive processes of bounded counts: How different are they?

Hee-Young Kim,Tobias A Möller,Christian H Weiß

doi:10.1007/s00180-020-00980-6

Hee-Young Kim, Tobias A Möller + Show 1 more

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https://doi.org/10.1007/s00180-020-00980-6

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Abstract

We focus on purely autoregressive (AR)-type models defined on the bounded range {0,1,ldots , n} with a fixed upper limit n in mathbb {N}. These include the binomial AR model, binomial AR conditional heteroscedasticity (ARCH) model, binomial-variation AR model with their linear conditional mean, nonlinear max-binomial AR model, and binomial logit-ARCH model. We consider the key problem of identifying which of these AR-type models is the true data-generating process. Despite the volume of the literature on model selection, little is known about this procedure in the context of nonnested and nonlinear time series models for counts. We consider the most popular approaches used for model identification, Akaike’s information criterion and the Bayesian information criterion, and compare them using extensive Monte Carlo simulations. Furthermore, we investigate the properties of the fitted models (both the correct and wrong models) obtained using maximum likelihood estimation. A real-data example demonstrates our findings.

Highlights

Count time series occur in various fields, including investigations of natural phenomena (e. g., rare disease occurrences, animal sightings, and severe weather events) and in economic contexts (e. g., monitoring the number of transactions)
We consider the most popular approaches used for model identification, Akaike’s information criterion and the Bayesian information criterion, and compare them using extensive Monte Carlo simulations
The first and main part of our study focusses on the conditional linear AR (CLAR)-type models introduced in Sect. 2; the corresponding datagenerating process (DGP) scenarios are summarized in Tables 1 and 2

Summary

Introduction

Count time series occur in various fields, including investigations of natural phenomena (e. g., rare disease occurrences, animal sightings, and severe weather events) and in economic contexts (e. g., monitoring the number of transactions). Count time series occur in various fields, including investigations of natural phenomena G., rare disease occurrences, animal sightings, and severe weather events) and in economic contexts Has been made in modeling count time series over the last 20 years; see Weiß (2018). The most popular stationary count time series models are arguably the integer-valued autoregressive moving-average (INARMA) models, dating back to McKenzie (1985) and Al-Osh and Alzaid (1987), which use a probabilistic operator called binomial thinning. The simplest INARMA model is the integer-valued autoregressive model of order one, abbreviated as INAR(1).

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