73 research outputs found
Interventions in ingarch processes
We study the problem of intervention effects generating various types of outliers in a linear count time series model. This model belongs to the class of observation driven models and extends the class of Gaussian linear time series models within the exponential family framework. Studies about effects of covariates and interventions for count time series models have largely fallen behind due to the fact that the underlying process, whose behavior determines the dynamics of the observed process, is not observed. We suggest a computationally feasible approach to these problems, focusing especially on the detection and estimation of sudden shifts and outliers. To identify successfully such unusual events we employ the maximum of score tests, whose critical values in finite samples are determined by parametric bootstrap. The usefulness of the proposed methods is illustrated using simulated and real data examples. --parametric bootstrap,generalized linear models,observation driven models,level shifts,transient shifts,outliers
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
Model selection for time series of count data
This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordSelecting between competing statistical models is a challenging problem especially when the competing
models are non-nested. An effective algorithm is developed in a Bayesian framework for
selecting between a parameter-driven autoregressive Poisson regression model and an observationdriven
integer valued autoregressive model when modeling time series count data. In order to achieve
this a particle MCMC algorithm for the autoregressive Poisson regression model is introduced. The
particle filter underpinning the particle MCMC algorithm plays a key role in estimating the marginal
likelihood of the autoregressive Poisson regression model via importance sampling and is also utilised
to estimate the DIC. The performance of the model selection algorithms are assessed via a simulation
study. Two real-life data sets, monthly US polio cases (1970-1983) and monthly benefit claims
from the logging industry to the British Columbia Workers Compensation Board (1985-1994) are
successfully analysed
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