4 research outputs found
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
Modeling threshold conditional heteroscedasticity with regime-dependent skewness and kurtosis
Construction of nonlinear time series models with a flexible probabilistic structure is an important challenge for statisticians. Applications of such a time series model include ecology, economics and finance. In this paper we consider a threshold model for all the first four conditional moments of a time series. The nonlinear structure in the conditional mean is specified by a threshold autoregression and that of the conditional variance by a threshold generalized autoregressive conditional heteroscedastic (GARCH) model. There are many options for the conditional innovation density in the modeling of the skewness and kurtosis such as the GramCharlier (GC) density and the skewed-t density. The GramCharlier (GC) density allows explicit modeling of the skewness and kurtosis parameters and therefore is the main focus of this paper. However, its performance is compared with that of Hansen's skewed-t distribution in the data analysis section of the paper. The regime-dependent feature for the first four conditional moments allows more flexibility in modeling and provides better insights into the structure of a time series. A Lagrange multiplier (LM) test is developed for testing for the presence of threshold structure. The test statistic is similar to the classical tests for the presence of a threshold structure but allowing for a more general regime-dependent structure. The new model and the LM test are illustrated using the Dow Jones Industrial Average, the Hong Kong Hang Seng Index and the Yen/US exchange rate. © 2011 Elsevier B.V. All rights reserved.link_to_subscribed_fulltex
Modeling threshold conditional heteroscedasticity with regime-dependent skewness and kurtosis
Construction of nonlinear time series models with a flexible probabilistic structure is an important challenge for statisticians. Applications of such a time series model include ecology, economics and finance. In this paper we consider a threshold model for all the first four conditional moments of a time series. The nonlinear structure in the conditional mean is specified by a threshold autoregression and that of the conditional variance by a threshold generalized autoregressive conditional heteroscedastic (GARCH) model. There are many options for the conditional innovation density in the modeling of the skewness and kurtosis such as the Gram-Charlier (GC) density and the skewed-t density. The Gram-Charlier (GC) density allows explicit modeling of the skewness and kurtosis parameters and therefore is the main focus of this paper. However, its performance is compared with that of Hansen's skewed-t distribution in the data analysis section of the paper. The regime-dependent feature for the first four conditional moments allows more flexibility in modeling and provides better insights into the structure of a time series. A Lagrange multiplier (LM) test is developed for testing for the presence of threshold structure. The test statistic is similar to the classical tests for the presence of a threshold structure but allowing for a more general regime-dependent structure. The new model and the LM test are illustrated using the Dow Jones Industrial Average, the Hong Kong Hang Seng Index and the Yen/US exchange rate.Gram-Charlier density Kurtosis Lagrange multiplier test Skewness TGARCH-GC model Threshold GARCH model