On autocorrelation in a Poisson regression model

Davis, Richard A.; Dunsmuir, William T. M.; Wang, Ying

doi:10.1093/biomet/87.3.491

Cited by 105 publications

(150 citation statements)

References 9 publications

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“…This conclusion has recently been confirmed by Jung and Liesenfeld (2001) using an approximation to maximum likelihood estimation in a parameter driven model. Davis et al (1999Davis et al ( , 2000 also report on a preliminary analysis of a series of daily counts of patients presenting at the accident and emergency department of Campbelltown Hospital located in the southwest metropolitan area of Sydney, Australia. Here we extend that analysis with a more comprehensive model for the seasonal effects and the pollution series.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…The final model is summarized in The fitted values from the model are shown in Figure 2 along with the actual counts. In this final model, various test statistics reviewed in Davis et al (1999Davis et al ( , 2000 for the presence of a latent process and the degree of autocorrelation indicated that there was no need to include additional autoregressive or moving average terms.…”

Section: Fitting the Modelmentioning

confidence: 98%

“…In exploratory analysis rainfall did not appear to play a major role, whereas humidity did with an approximate lag of 14 days. Details of the construction and statistical significance of this variable are provided in Davis et al (2000). This model may not be appropriate because the intensity of seasonal peaks appears to vary considerably from year to year.…”

Section: Meteorological Datamentioning

confidence: 99%

See 2 more Smart Citations

Observation-driven models for Poisson counts

Davis¹,

Dunsmuir²,

Streett³

2003

Biometrika

233

217

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This paper is concerned with a general class of observation driven models for time series of counts whose conditional distributions given past observations and explanatory variables follow a Poisson distribution. These models provide a flexible framework for modeling a wide range of dependence structures. Conditions for stationarity and ergodicity of these processes are established from which the large sample properties of the maximum likelihood estimators can be derived. Simulations are provided to give additional insight into the finite sample behavior of the estimates. Finally an application to a regression model for daily counts of accident and emergency room presentations for asthma at several Sydney hospitals is described.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Fitting the Modelmentioning

confidence: 98%

Section: Meteorological Datamentioning

confidence: 99%

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Observation-driven models for Poisson counts

Davis¹,

Dunsmuir²,

Streett³

2003

Biometrika

233

217

View full text Add to dashboard Cite

show abstract

“…Davis, Dunsmuir & Wang (2000) discuss several applications of Poisson regression in time series with serial dependence arising in public health: a series of T = 168 monthly polio counts and a series of T = 1465 daily asthma counts. The dimension of the integral, d = T , corresponds to the length of the time series -potentially in the hundreds or thousands.…”

Section: Figure 1: Respiratory Infection Indicator (0=absent 1=presementioning

confidence: 99%

Quasi-Monte Carlo for Highly Structured Generalised Response Models

Kuo

Dunsmuir

Sloan

et al. 2007

Methodol Comput Appl Probab

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Highly structured generalised response models, such as generalised linear mixed models and generalised linear models for time series regression, have become an indispensable vehicle for data analysis and inference in many areas of application. However, their use in practice is hindered by high-dimensional intractable integrals. Quasi-Monte Carlo (QMC) is a dynamic research area in the general problem of high-dimensional numerical integration, although its potential for statistical applications is yet to be fully explored. We survey recent research in QMC, particularly lattice rules, and report on its application to highly structured generalised response models. New challenges for QMC are identified and new methodologies are developed. QMC methods are seen to provide significant improvements compared with ordinary Monte Carlo methods. ABSTRACTHighly structured generalised response models, such as generalised linear mixed models and generalised linear models for time series regression, have become an indispensable vehicle for data analysis and inference in many areas of application. However, their use in practice is hindered by high-dimensional intractable integrals. Quasi-Monte Carlo (QMC) is a dynamic research area in the general problem of high-dimensional numerical integration, although its potential for statistical applications is yet to be fully explored. We survey recent research in QMC, particularly lattice rules, and report on its application to highly structured generalised response models. New challenges for QMC are identified and new methodologies are developed. QMC methods are seen to provide significant improvements compared with ordinary Monte Carlo methods.

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“…The data are published by the United States (US) Centers for Disease Control and consist of 168 observations with some strongly deviating data points. This data set has been previously studied by many researchers, including Zeger (1988), Davis et al (2000) and Jung and Tremayne (2011). Recently, Kang and Lee (2014) performed the CUSUM test to detect change points in this data based on Poisson autoregressive models.…”

Section: Introductionmentioning

confidence: 99%

Robust CUSUM test for time series of counts and its application to analyzing the polio incidence data

Kang¹

2015

Journal of the Korean Data and Information Science Society

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In this paper, we analyze the polio incidence data based on the Poisson autoregressive models, focusing particularly on change-point detection. Since the data include some strongly deviating observations, we employ the robust cumulative sum (CUSUM) test proposed by Kang and Song (2015) to perform the test for parameter change. Contrary to the result of Kang and Lee (2014), our data analysis indicates that there is no significant change in the case of the CUSUM test with strong robustness and the same result is obtained after ridding the polio data of outliers. We additionally consider the comparison of the forecasting performance. All the results demonstrate that the robust CUSUM test performs adequately in the presence of seemingly outliers.Keywords: Minimum density power divergence estimator, Poisson autoregressive model, robust parameter change test, the polio incidence data.

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On autocorrelation in a Poisson regression model

Cited by 105 publications

References 9 publications

Observation-driven models for Poisson counts

Observation-driven models for Poisson counts

Quasi-Monte Carlo for Highly Structured Generalised Response Models

Robust CUSUM test for time series of counts and its application to analyzing the polio incidence data

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