Seasonal Count Time Series

TL;DR

This paper introduces a flexible seasonal count time series model that accommodates any marginal distribution, complex autocorrelations, and covariates, with methods for inference and demonstrated effectiveness through simulations and real data application.

Contribution

It develops a novel modeling framework for seasonal count time series using Gaussian process transformations, enabling flexible autocorrelation structures and likelihood-based inference.

Findings

Model effectively captures seasonal patterns in count data.

Likelihood inference methods are successfully applied.

Simulation and real data demonstrate model's practical utility.

Abstract

Count time series are widely encountered in practice. As with continuous valued data, many count series have seasonal properties. This paper uses a recent advance in stationary count time series to develop a general seasonal count time series modeling paradigm. The model permits any marginal distribution for the series and the most flexible autocorrelations possible, including those with negative dependence. Likelihood methods of inference can be conducted and covariates can be easily accommodated. The paper first develops the modeling methods, which entail a discrete transformation of a Gaussian process having seasonal dynamics. Properties of this model class are then established and particle filtering likelihood methods of parameter estimation are developed. A simulation study demonstrating the efficacy of the methods is presented and an application to the number of rainy days in successive weeks in Seattle, Washington is given.