Time-Varying Poisson Autoregression

TL;DR

This paper introduces a novel time-varying Poisson autoregressive model with exogenous variables (TV-PARX) that effectively captures complex dynamics and structural breaks in count time series, with proven theoretical properties and practical applications.

Contribution

The paper develops the TV-PARX model using a score-driven framework, demonstrating its ability to model nonlinear dynamics and structural breaks in count data.

Findings

Model has strong consistency and asymptotic normality under mild conditions.

Finite-sample simulations show high forecasting accuracy.

Empirical analysis of COVID-19 and US corporate defaults illustrates practical usefulness.

Abstract

In this paper we propose a new time-varying econometric model, called Time-Varying Poisson AutoRegressive with eXogenous covariates (TV-PARX), suited to model and forecast time series of counts. {We show that the score-driven framework is particularly suitable to recover the evolution of time-varying parameters and provides the required flexibility to model and forecast time series of counts characterized by convoluted nonlinear dynamics and structural breaks.} We study the asymptotic properties of the TV-PARX model and prove that, under mild conditions, maximum likelihood estimation (MLE) yields strongly consistent and asymptotically normal parameter estimates. Finite-sample performance and forecasting accuracy are evaluated through Monte Carlo simulations. The empirical usefulness of the time-varying specification of the proposed TV-PARX model is shown by analyzing the number of new daily COVID-19 infections in Italy and the number of corporate defaults in the US.