Detecting Serial Dependence in Binomial Time Series II: Observation Driven Models

TL;DR

This paper develops score-type statistical tests for detecting serial dependence in binary time series, especially within observation-driven models like GLARMA and BARMA, facilitating easier practical application.

Contribution

It introduces new score tests for serial dependence detection in binomial time series models, including a supremum test for nuisance parameters, enhancing practical assessment methods.

Findings

Tests can be applied using standard logistic regression.

Supremum test effectively handles nuisance parameters.

Method improves detection of serial dependence in binary data.

Abstract

The detection of serial dependence in binary or binomial valued time series is difficult using standard time series methods, particularly when there are regression effects to be modelled. In this paper we derive score-type tests for detecting departures from independence in the directions of the GLARMA\ and BARMA\ type observation driven models. These score tests can easily be applied using a standard logistic regression and so may have appeal to practitioners who wish to initially assess the need to incorporate serial dependence effects. To deal with the nuisance parameters in some GLARMA models a supremum type test is implemented.