A log-linear model for non-stationary time series of counts

TL;DR

This paper introduces a novel log-linear model for non-stationary count time series with strong trends, leveraging scale-invariant distributions and proving absolute regularity for statistical applications.

Contribution

It presents a new nonstationary count time series model based on scale-invariant families, differing from Poisson-INGARCH, and establishes its statistical properties.

Findings

Model suitable for data with strong trends

Proves absolute regularity with exponential decay

Offers a flexible alternative to Poisson-INGARCH

Abstract

We propose a new model for nonstationary integer-valued time series which is particularly suitable for data with a strong trend. In contrast to popular Poisson-INGARCH models, but in line with classical GARCH models, we propose to pick the conditional distributions from nearly scale invariant families where the mean absolute value and the standard deviation are of the same order of magnitude. As an important prerequisite for applications in statistics, we prove absolute regularity of the count process with exponentially decaying coefficients.