Statistical Modelling 24 (1) (2024), 2957
Bayesian modelling of integer-valued transfer function models
Aljo Clair Pingal,
Department of Statistics,
Feng Chia University,
Taichung,
Taiwan.
Cathy W. S. Chen,
Department of Statistics,
Feng Chia University,
Taichung,
Taiwan.
e-mail: chenws@mail.fcu.edu.tw
Abstract:
External events are commonly known as interventions that often affect times series of counts.
This research introduces a class of transfer function models that include four different types of interventions
on integer-valued time series: abrupt start and abrupt decay (additive outlier), abrupt start
and gradual decay (transient shift), abrupt start and permanent effect (level shift) and gradual start
and permanent effect. We propose integer-valued transfer function models incorporating a generalized
Poisson, log-linear generalized Poisson or negative binomial to estimate and detect these four types of
interventions in a time series of counts. Utilizing Bayesian methods, which are adaptive Markov chain
Monte Carlo (MCMC) algorithms to obtain the estimation, we further employ deviance information
criterion (DIC), posterior odd ratios and mean squared standardized residual for model comparisons.
As an illustration, this study evaluates the effectiveness of our methods through a simulation study
and application to crime data in Albury City, New South Wales (NSW) Australia. Simulation results
show that the MCMC procedure is reasonably effective. The empirical outcome also reveals that the
proposed models are able to successfully detect the locations and type of interventions.
Keywords:
Bayesian methods, intervention analysis, generalized Poisson, integer-valued GARCH
model, Markov chain Monte Carlo method, transfer function
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