TY - JOUR

T1 - Interventions in log-linear Poisson autoregression

AU - Fokianos, K.

AU - Fried, R.

PY - 2012/8

Y1 - 2012/8

N2 - We consider the problem of estimating and detecting outliers in count time series data following a log-linear observation driven model. Log-linear models for count time series arise naturally because they correspond to the canonical link function of the Poisson distribution. They yield both positive and negative dependence, and covariate information can be conveniently incorporated. Within this framework, we establish test procedures for detection of unusual events (‘interventions’) leading to different kinds of outliers, we implement joint maximum likelihood estimation of model parameters and outlier sizes and we derive formulae for correcting the data for detected interventions. The effectiveness of the proposed methodology is illustrated with two real data examples. The first example offers a fresh data analytic point of view towards the polio data. Our methodology identifies different forms of outliers in these data by an observation-driven model. The second example deals with some campylobacterosis data which we analyzed in a previous communication, by a different model. The results are reconfirmed by the new model that we put forward in this communication. The reliability of the procedure is verified using artificial data examples.

AB - We consider the problem of estimating and detecting outliers in count time series data following a log-linear observation driven model. Log-linear models for count time series arise naturally because they correspond to the canonical link function of the Poisson distribution. They yield both positive and negative dependence, and covariate information can be conveniently incorporated. Within this framework, we establish test procedures for detection of unusual events (‘interventions’) leading to different kinds of outliers, we implement joint maximum likelihood estimation of model parameters and outlier sizes and we derive formulae for correcting the data for detected interventions. The effectiveness of the proposed methodology is illustrated with two real data examples. The first example offers a fresh data analytic point of view towards the polio data. Our methodology identifies different forms of outliers in these data by an observation-driven model. The second example deals with some campylobacterosis data which we analyzed in a previous communication, by a different model. The results are reconfirmed by the new model that we put forward in this communication. The reliability of the procedure is verified using artificial data examples.

KW - generalized linear models

KW - level shifts

KW - likelihood

KW - link function

KW - observation-driven models

KW - outlier detection

KW - parametric bootstrap

KW - power

KW - transient shifts

U2 - 10.1177/1471082X1201200401

DO - 10.1177/1471082X1201200401

M3 - Journal article

VL - 12

SP - 299

EP - 322

JO - Statistical Modelling

JF - Statistical Modelling

SN - 1471-082X

IS - 4

ER -