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GQL Versus Conditional GQL Inferences for Non‐Stationary Time Series of Counts with Overdispersion

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  • Taslim S. Mallick
  • Brajendra C. Sutradhar

Abstract

. This article proposes an autoregressive model for time series of counts with non‐stationary means, variances and covariances as functions of certain time‐dependant covariates. For the estimation of the regression, overdispersion and correlation index parameters, a conditional generalized quasilikelihood (CGQL) approach is developed under the assumption that the count responses marginally satisfy the first two moments of a negative binomial distribution. Thus this CGQL approach avoids the use of the likelihood or so‐called partial likelihood of the data which are known to be extremely complicated in the present non‐stationary time series set‐up. It is shown through an extensive simulation study that the proposed CGQL approach performs very well in estimating the parameters of the model. This is also shown that the CGQL approach performs better than an existing GQL approach, especially for the estimation of the overdispersion parameter of the model.

Suggested Citation

  • Taslim S. Mallick & Brajendra C. Sutradhar, 2008. "GQL Versus Conditional GQL Inferences for Non‐Stationary Time Series of Counts with Overdispersion," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 402-420, March.
    • Handle: RePEc:bla:jtsera:v:29:y:2008:i:2:p:402-420
    DOI: 10.1111/j.1467-9892.2007.00570.x
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    Cited by:

    1. Yuvraj Sunecher & Naushad Mamode Khan & Miroslav M. Ristić & Vandna Jowaheer, 2019. "BINAR(1) negative binomial model for bivariate non-stationary time series with different over-dispersion indices," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 625-653, December.
    2. R. Prabhakar Rao & Brajendra C. Sutradhar, 2020. "Multiple Categorical Covariates-Based Multinomial Dynamic Response Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 186-219, February.
    3. Pushpakanthie Wijekoon & Alwell Oyet & Brajendra C. Sutradhar, 2019. "Pair-Wise Family-Based Correlation Model for Spatial Count Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 133-184, June.
    4. Brajendra C. Sutradhar & Vandna Jowaheer & R. Prabhakar Rao, 2016. "Semi-Parametric Models for Negative Binomial Panel Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 269-303, August.
    5. Brajendra C. Sutradhar & R. Prabhakar Rao, 2016. "Inferences in Longitudinal Count Data Models with Measurement Errors in Time Dependent Covariates," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(1), pages 39-65, May.

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