Modelling interventions in INGARCH processes

We study different approaches to describe intervention effects within the framework of integer-valued GARCH (INGARCH) models for time series of counts. Fokianos and Fried (J. Time Ser. Anal. 2010, 31: 210–225) treat a model where an intervention affects the non-observable underlying mean process at the time point of its occurrence and additionally the whole process thereafter via its dynamics. As an alternative, we consider a model where an intervention directly affects the observation at the time point of its occurrence, but not the underlying mean, and then also enters the dynamics of the process. While the former definition describes an internal change, the latter can be understood as an external effect on the observations due to e.g. immigration. For our alternative model we develop conditional likelihood estimation and, based on this, tests and detection procedures for intervention effects. Both models are compared analytically and using simulated and real data examples. We study the effect of misspecification on the fitted intervention model. Special attention is paid to computational issues

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

Bayesian outlier detection in INGARCH time series

INGARCH models for time series of counts arising, e.g., in epidemiology assume the observations to be Poisson distributed conditionally on the past, with the conditional mean being an affinelinear function of the previous observations and the previous conditional means. We model outliers within such processes, assuming that we observe a contaminated process with additive Poisson distributed contamination, affecting each observation with a small probability. Our particular concern are additive outliers, which do not enter the dynamics of the process and can represent measurement artifacts and other singular events influencing a single observation. Such outliers are difficult to handle within a non-Bayesian framework since the uncontaminated values entering the dynamics of the process at contaminated time points are unobserved. We propose a Bayesian approach to outlier modeling in INGARCH processes, approximating the posterior distribution of the model parameters by application of a componentwise Metropolis- Hastings algorithm. Analyzing real and simulated data sets, we find Bayesian outlier detection with non-informative priors to work well if there are some outliers in the data

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

Modelling asthma cases using count analysis approach: poisson INGARCH and negative binomial INGARCH

Pollution in Johor Bahru is an issue that needs adequate attention because it has contributed to a number of asthma cases in the area. Therefore, the goal of this study is to investigate the behaviour of asthma disease in Johor Bahru by count analysis approaches namely; Poisson Integer Generalized Autoregressive Conditional Heteroscedasticity (Poisson-INGARCH) and Negative Binomial INGARCH (NB-INGARCH) with identity and log link function. The estimation of the parameter was done by quasi-maximum likelihood estimation. Model assessment was evaluated from the Pearson residuals, cumulative periodogram, the probability integral transform (PIT) histogram, log-likelihood value, Akaike’s Information Criterion (AIC) and Bayesian information criterion (BIC). Our result shows that NB-INGARCH with identity and log link function is adequate in representing the asthma data with uncorrelated Pearson residuals, higher in log likelihood, the PIT exhibits normality yet the lowest AIC and BIC. However, in terms of forecasting accuracy, NB-INGARCH with identity link function performed better with the smaller RMSE (8.54) for the sample data. Therefore, NB- INGARCH with identity link function can be applied as the prediction model for asthma disease in Johor Bahru. Ideally, this outcome can assist the Department of Health in executing counteractive action and early planning to curb asthma diseases in Johor Bahru

tscount: An R package for analysis of count time series following generalized linear models

The R package tscount provides likelihood-based estimation methods for analysis and modelling of count time series following generalized linear models. This is a exible class of models which can describe serial correlation in a parsimonious way. The conditional mean of the process is linked to its past values, to past observations and to potential covariate e ects. The package allows for models with the identity and with the logarithmic link function. The conditional distribution can be Poisson or Negative Binomial. An important special case of this class is the so-called INGARCH model and its log-linear extension. The package includes methods for model tting and assessment, prediction and intervention analysis. This paper summarizes the theoretical background of these methods with references to the literature for further details. It gives details on the implementation of the package and provides simulation results for models which have not been studied theoretically before. The usage of the package is demonstrated by two data examples