Self-excited Threshold Poisson Autoregression

This paper studies theory and inference of an observation-driven model for time series of counts. It is assumed that the observations follow a Poisson distribution conditioned on an accompanying intensity process, which is equipped with a two-regime structure according to the magnitude of the lagged observations. The model remedies one of the drawbacks of the Poisson autoregression model by allowing possibly negative correlation in the observations. Classical Markov chain theory and Lyapunov's method are utilized to derive the conditions under which the process has a unique invariant probability measure and to show a strong law of large numbers of the intensity process. Moreover the asymptotic theory of the maximum likelihood estimates of the parameters is established. A simulation study and a real data application are considered, where the model is applied to the number of major earthquakes in the world

Self-Excited Threshold Poisson Autoregression

This article studies theory and inference of an observation-driven model for time series of counts. It is assumed that the observations follow a Poisson distribution conditioned on an accompanying intensity process, which is equipped with a two-regime structure according to the magnitude of the lagged observations. Generalized from the Poisson autoregression, it allows more flexible, and even negative correlation, in the observations, which cannot be produced by the single-regime model. Classical Markov chain theory and Lyapunov’s method are used to derive the conditions under which the process has a unique invariant probability measure and to show a strong law of large numbers of the intensity process. Moreover, the asymptotic theory of the maximum likelihood estimates of the parameters is established. A simulation study and a real-data application are considered, where the model is applied to the number of major earthquakes in the world. Supplementary materials for this article are available online.postprin

An Integer GARCH model for a Poisson process with time varying zero-inflation

A time-varying zero-inflated serially dependent Poisson process is proposed. The model assumes that the intensity of the Poisson Process evolves according to a generalized autoregressive conditional heteroscedastic (GARCH) formulation. The proposed model is a generalization of the zero-inflated Poisson Integer GARCH model proposed by Fukang Zhu in 2012, which in return is a generalization of the Integer GARCH (INGARCH) model introduced by Ferland, Latour, and Oraichi in 2006. The proposed model builds on previous work by allowing the zero-inflation parameter to vary over time, governed by a deterministic function or by an exogenous variable. Both the Expectation Maximization (EM) and the Maximum Likelihood Estimation (MLE) approaches are presented as possible estimation methods. A simulation study shows that both parameter estimation methods provide good estimates. Applications to two real-life data sets show that the proposed INGARCH model provides a better fit than the traditional zero-inflated INGARCH model in the cases considered

Monitoring Covid-19 contagion growth in Europe. CEPS Working Document No 2020/03, March 2020

We present an econometric model which can be employed to monitor the evolution of the COVID-19 contagion curve. The model is a Poisson autoregression of the daily new observed cases, and can dynamically show the evolution of contagion in different time periods and locations, allowing for the comparative evaluation of policy approaches. We present timely results for nine European countries currently hit by the virus. From the findings, we draw four main conclusions. First, countries experiencing an explosive process (currently France, Italy and Spain), combined with high persistence of contagion shocks (observed in most countries under investigation), require swift policy measures such as quarantine, diffuse testing and even complete lockdown. Second, in countries with high persistence but lower contagion growth (currently Germany) careful monitoring should be coupled with at least “mild” restrictions such as physical distancing or isolation of specific areas. Third, in some countries, such as Norway and Denmark, where trends seem to be relatively under control and depend on daily contingencies, with low persistence, the approach to restrictive measures should be more cautious since there is a risk that social costs outweigh the benefits. Fourth, countries with a limited set of preventive actions in place (such as the Netherlands, Switzerl