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On variance estimation in a negative binomial time series regression model

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  • Wu, Rongning

Abstract

We study variance estimation in a negative binomial regression model for analyzing time series of counts, where serial dependence among the observed counts is introduced by an autocorrelated latent process. The regression coefficient vector is estimated by maximizing the pseudo-likelihood with the latent process suppressed. The resulting estimator is referred to as the generalized linear model estimator, and its consistency and asymptotic normality have been established by Davis and Wu [R.A. Davis, R. Wu, A negative binomial model for time series of counts, Biometrika 96 (2009) 735–749] when the latent process is stationary and strongly mixing. However, in order to perform valid statistical inferences about the regression coefficients, it is essential to develop a consistent estimation procedure for the asymptotic covariance matrix of the generalized linear model estimator. We propose two types of estimators using kernel-based and subsampling methods, and establish their consistency property. The results can be generalized straightforwardly to time series following a parameter-driven generalized linear model. Simulation study is conducted to evaluate the finite sample performance of the estimation methods.

Suggested Citation

  • Wu, Rongning, 2012. "On variance estimation in a negative binomial time series regression model," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 145-155.
    • Handle: RePEc:eee:jmvana:v:112:y:2012:i:c:p:145-155
    DOI: 10.1016/j.jmva.2012.06.006
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    References listed on IDEAS

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    1. J. Durbin & S. J. Koopman, 2000. "Time series analysis of non‐Gaussian observations based on state space models from both classical and Bayesian perspectives," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 3-56.
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    3. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 407-417, October.
    4. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-972, July.
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    6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    7. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    8. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    9. West, Kenneth D., 1997. "Another heteroskedasticity- and autocorrelation-consistent covariance matrix estimator," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 171-191.
    10. Wu, Rongning & Cao, Jiguo, 2011. "Blockwise empirical likelihood for time series of counts," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 661-673, March.
    11. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 422-422, October.
    12. Richard A. Davis & Rongning Wu, 2009. "A negative binomial model for time series of counts," Biometrika, Biometrika Trust, vol. 96(3), pages 735-749.
    13. M. J. Campbell, 1994. "Time Series Regression for Counts: An Investigation into the Relationship between Sudden Infant Death Syndrome and Environmental Temperature," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 157(2), pages 191-208, March.
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    Cited by:

    1. William Dunsmuir & Jieyi He, 2017. "Marginal Estimation of Parameter Driven Binomial Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(1), pages 120-144, January.
    2. Rongning Wu & Yunwei Cui, 2014. "A Parameter-Driven Logit Regression Model For Binary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 462-477, August.

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