An integer-valued autoregressive process for seasonality

ABSTRACT

In this paper, we propose an integer-valued autoregressive process of order 1 for seasonality with period d and intra-seasonally dependent innovations ($\mathrm{S}\mathrm{I}\mathrm{N}\mathrm{A}\mathrm{R}(1{)}_d$). Model properties are provided for the univariate and multivariate representation of the process. A computationally fast estimation method, which is based on conditional least squares with parameter restrictions, is proposed for the multivariate model representation and compared with a likelihood-based estimation method via the Monte Carlo simulation. An empirical application for different types of Chicago crime data is carried out in order to assess whether the proposed model is able to capture adequately the seasonality patterns in non-synthetic data.

KEYWORDS:

• Count data
• multivariate INAR
• seasonality
• Copula
• Poisson distribution

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62M10
• 62H12

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 see https://data.cityofchicago.org/Public-Safety/Crimes-2001-to-present/ijzp-q8t2 for the latest data snapshot.