A Classification of Observation-Driven State-Space Count Models for Panel Data

TL;DR

This paper extends a classic observation-driven count data model to ensure variance stationarity, allowing for more flexible variance processes while maintaining analytical tractability, supported by simulations and numerical studies.

Contribution

It introduces a generalized variance-stationary extension of Harvey and Fernandes's (1989) model for count data, broadening its applicability.

Findings

The extended model can handle increasing, decreasing, or stationary variance processes.

Simulation results demonstrate the model's improved flexibility and performance.

Numerical studies confirm the tractability and robustness of the proposed extension.

Abstract

State-space models are widely used in many applications. In the domain of count data, one such example is the model proposed by Harvey and Fernandes (1989). Unlike many of its parameter-driven alternatives, this model is observation-driven, leading to closed-form expressions for the predictive density. In this paper, we demonstrate the need to extend the model of Harvey and Fernandes (1989) by showing that their model is not variance stationary. Our extension can accommodate for a wide range of variance processes that are either increasing, decreasing, or stationary, while keeping the tractability of the original model. Simulation and numerical studies are included to illustrate the performance of our method.