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We consider the problems of robust estimation and testing for a log-linear model with feedback for the analysis of count time series. We study inference for contaminated data with transient shifts, level shifts and additive outliers. It turns out that the case of additive outliers deserves special attention. We propose a robust method for estimating the regression coefficients in the presence of interventions. The resulting robust estimators are asymptotically normally distributed under some regularity conditions. A robust score type test statistic is also examined. The methodology is applied to real and simulated data. © 2015, Springer Science+Business Media Dordrecht. 19 3 337 361

We investigate the relationship between weak dependence and mixing for discrete valued processes. We show that weak dependence implies mixing conditions under natural assumptions. The results specialize to the case of Markov processes. Several examples of integer valued processes are discussed and their weak dependence properties are investigated by means of a contraction principle. In fact, we show the stronger result that the mixing coefficients for infinite memory weakly dependent models decay geometrically fast. Hence, all integer values models that we consider have weak dependence coefficients which decay geometrically fast. © 2012 Elsevier B.V. 82 11 1941 1948 Cited By :4

We study statistical properties of a class of non-linear models for regression analysis of count time series. Under mild conditions, it is shown that a perturbed version of the model is geometrically ergodic and possesses moments of any order. This result turns out to be instrumental on deriving large sample properties of the maximum likelihood estimators of the regression parameters. The theory is illustrated with examples. © The Institute of Statistical Mathematics, Tokyo 2012. 64 6 1205 1225 Cited By :20

We investigated the problem of testing equality among spectral densities of several independent stationary processes. Our main methodological contribution is the introduction of a novel semiparametric log-linear model that links all of the spectral densities under consideration. This model is motivated by the asymptotic properties of the periodogram ordinates and specifies that the logarithmic ratio of G - 1 spectral density functions with respect to the Gth is linear in someparameters. Then the problem of testing equality of several spectral density functions is reducedto a parametric problem. Under this assumption, the large-sample theory of the maximum likelihoodestimator was studied, and it was found that the estimator is asymptotically normal even when themodel is misspecified. The development of the asymptotic theory is based on a new contrast function that might be useful for other spectral domain time series problems. The results are applicable to a variety of models, including linear and nonlinear processes. Simulations and data analysissupport further the theoretical findings. © 2008 American Statistical Association and the American Society for Quality. 50 3 317 331

We consider the problem of assessing prediction for count time series based on either the Poisson distribution or the negative binomial distribution. By a suitable parametrization we employ both distributions with the same mean. We regress the mean on its past values and the values of the response and after obtaining consistent estimators of the regression parameters, regardless of the response distribution, we employ different criteria to study the prediction problem. We show by simulation and data examples that scoring rules and diagnostic graphs that have been proposed for independent but not identically distributed data can be adapted in the setting of count dependent data. © 2013, © 2013 Taylor & Francis. 85 2 357 373 Cited By :4

Saddlepoint techniques have been used successfully in many applications, owing to the high accuracy with which they can approximate intractable densities and tail probabilities. This article concerns their use for the estimation of high-order integer-valued autoregressive, INAR(p), processes. Conditional least squares estimation and maximum likelihood estimation have been proposed for INAR(p) models, but the first is inefficient for estimating parametric models, and the second becomes difficult to implement as the order p increases. We propose a simple saddlepoint approximation to the log-likelihood that performs well even in the tails of the distribution and with complicated INAR models. We consider Poisson and negative binomial innovations, and show empirically that the estimator that maximises the saddlepoint approximation behaves very similarly to the maximum likelihood estimator in realistic settings. The approach is applied to data on meningococcal disease counts. Supplementary materials for this article are available online. © 2015, © American Statistical Association. 110 511 1229 1238

We are studying a novel class of goodness-of-fit tests for parametric count time series regression models. These test statistics are formed by considering smoothed versions of the empirical process of the Pearson residuals. Our construction yields test statistics which are consistent against Pitman's local alternatives and they converge weakly at the usual parametric rate. To approximate the asymptotic null distribution of the test statistics, we propose a parametric bootstrap method and we study its properties. The methodology is applied to simulated and real data. 7 1 793 819 Cited By :7

INGARCH models for time series of counts arising, e.g., in epidemiology or finance assume the observations to be Poisson distributed conditionally on the past, with the conditional mean being an affine-linear 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. Retrospective analysis of such outliers is difficult 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 in practice when there are some outliers in the data. © 2013, Springer Science+Business Media New York. 25 2 365 374 Cited By :5

We consider generalized linear models for regression modeling of count time series. We give easily verifiable conditions for obtaining weak dependence for such models. These results enable the development of maximum likelihood inference under minimal conditions. Some examples which are useful to applications are discussed in detail. © 2012 Elsevier B.V.. 82 5 942 948 Cited By :32

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. © 2012 SAGE Publications. 12 4 299 322 Cited By :9

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We consider m distributions in which the first m-1 are obtained by multiplicative exponential distortions of the mth distribution, which is a reference. The combined data from rn samples, one from each distribution, are used in the semiparametric large-sample problem of estimating each distortion and the reference distribution and testing the hypothesis that the distributions are identical. The approach generalizes the classical normal-based one-way analysis of variance in the sense that it obviates the need for a completely specified parametric model. An advantage is that the probability density of the reference distribution is estimated from the combined data and not only from the mth sample. A power comparison with the t and F tests and with two nonparametric tests, obtained by means of a simulation, points to the merit of the present approach. The method is applied to rain-rate data from meteorological instruments. 43 1 56 65 Cited By :54