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Blockwise empirical likelihood for time series of counts

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  • Wu, Rongning
  • Cao, Jiguo
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    Abstract

    Time series of counts have a wide variety of applications in real life. Analyzing time series of counts requires accommodations for serial dependence, discreteness, and overdispersion of data. In this paper, we extend blockwise empirical likelihood (Kitamura, 1997 [15]) to the analysis of time series of counts under a regression setting. In particular, our contribution is the extension of Kitamura's (1997) [15] method to the analysis of nonstationary time series. Serial dependence among observations is treated nonparametrically using a blocking technique; and overdispersion in count data is accommodated by the specification of a variance-mean relationship. We establish consistency and asymptotic normality of the maximum blockwise empirical likelihood estimator. Simulation studies show that our method has a good finite sample performance. The method is also illustrated by analyzing two real data sets: monthly counts of poliomyelitis cases in the USA and daily counts of non-accidental deaths in Toronto, Canada.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 102 (2011)
    Issue (Month): 3 (March)
    Pages: 661-673

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    Handle: RePEc:eee:jmvana:v:102:y:2011:i:3:p:661-673

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    Related research

    Keywords: Autocorrelation Generalized linear model Latent process Nonstationarity Overdispersion Regression analysis;

    References

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    1. Francesco Bravo, 2009. "Blockwise generalized empirical likelihood inference for non-linear dynamic moment conditions models," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 208-231, 07.
    2. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-20, May.
    3. Daniel J. Nordman & Philipp Sibbertsen & Soumendra N. Lahiri, 2007. "Empirical likelihood confidence intervals for the mean of a long-range dependent process," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(4), pages 576-599, 07.
    4. de Jong, R.M., 1995. "Laws of Large Numbers for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 11(02), pages 347-358, February.
    5. Richard A. Davis & Rongning Wu, 2009. "A negative binomial model for time series of counts," Biometrika, Biometrika Trust, vol. 96(3), pages 735-749.
    6. Davidson, James, 1992. "A Central Limit Theorem for Globally Nonstationary Near-Epoch Dependent Functions of Mixing Processes," Econometric Theory, Cambridge University Press, vol. 8(03), pages 313-329, September.
    7. Chan, Ngai Hang & Ling, Shiqing, 2006. "Empirical Likelihood For Garch Models," Econometric Theory, Cambridge University Press, vol. 22(03), pages 403-428, June.
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    Cited by:
    1. Daniel J. Nordman & Helle Bunzel & Soumendra N. Lahiri, 2012. "A Non-standard Empirical Likelihood for Time Series," CREATES Research Papers 2012-55, School of Economics and Management, University of Aarhus.

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