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Generalized linear autoregressions

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  • Neil Shephard

Abstract

This paper develops a class of autoregressive and moving average models which extend the generalized linear model. Likelihood and quasi-likelihood estimation procedures are developed which allow the models to be easily estimated and tested. Several examples are given which illustrate the usefulness and simplicity of the approach advocated in this paper.

Suggested Citation

  • Neil Shephard, 1995. "Generalized linear autoregressions," Economics Papers 8., Economics Group, Nuffield College, University of Oxford.
    • Handle: RePEc:nuf:econwp:0008
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    File URL: http://www.nuff.ox.ac.uk/economics_wp/w8/glar.zip
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    References listed on IDEAS

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    1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    2. 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. Dionne, Georges & Zhou, Xiaozhou, 2016. "The Dynamics of Ex-ante High-Frequency Liquidity: An Empirical Analysis," Working Papers 15-5, HEC Montreal, Canada Research Chair in Risk Management.
    2. Snyder, Ralph D. & Ord, J. Keith & Beaumont, Adrian, 2012. "Forecasting the intermittent demand for slow-moving inventories: A modelling approach," International Journal of Forecasting, Elsevier, vol. 28(2), pages 485-496.
    3. Katarzyna Bien & Ingmar Nolte & Winfried Pohlmeier, 2011. "An inflated multivariate integer count hurdle model: an application to bid and ask quote dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(4), pages 669-707, June.
    4. Peng, Rong & Lu, Zudi, 2024. "Semiparametric Averaging of Nonlinear Marginal Logistic Regressions and Forecasting for Time Series Classification," Econometrics and Statistics, Elsevier, vol. 31(C), pages 19-37.
    5. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2006. "Vector Multiplicative Error Models: Representation and Inference," NBER Working Papers 12690, National Bureau of Economic Research, Inc.
    6. Jung, Robert & Kukuk, Martin & Liesenfeld, Roman, 2005. "Time Series of Count Data: Modelling and Estimation," Economics Working Papers 2005-08, Christian-Albrechts-University of Kiel, Department of Economics.
    7. Robert Jung & A. Tremayne, 2011. "Useful models for time series of counts or simply wrong ones?," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(1), pages 59-91, March.
    8. Katarzyna Bien & Ingmar Nolte & Winfried Pohlmeier, 2008. "A multivariate integer count hurdle model: theory and application to exchange rate dynamics," Studies in Empirical Economics, in: Luc Bauwens & Winfried Pohlmeier & David Veredas (ed.), High Frequency Financial Econometrics, pages 31-48, Springer.
    9. Katarzyna Bień-Barkowska, 2012. "A Bivariate Copula-based Model for a Mixed Binary-Continuous Distribution: A Time Series Approach," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 4(2), pages 117-142, June.
    10. Ralph D. Snyder & Gael M. Martin & Phillip Gould & Paul D. Feigin, 2007. "An Assessment of Alternative State Space Models for Count Time Series," Monash Econometrics and Business Statistics Working Papers 4/07, Monash University, Department of Econometrics and Business Statistics.
    11. Babii, Andrii & Chen, Xi & Ghysels, Eric, 2019. "Commercial and Residential Mortgage Defaults: Spatial Dependence with Frailty," Journal of Econometrics, Elsevier, vol. 212(1), pages 47-77.
    12. Marinho G. Andrade & Katiane S. Conceição & Nalini Ravishanker, 2024. "Zero-modified count time series modeling with an application to influenza cases," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(3), pages 611-637, September.
    13. Jeffrey R. Russell & Robert F. Engle, 1998. "Econometric Analysis of Discrete-valued Irregularly-spaced Financial Transactions Data Using a New Autoregressive Conditional Multinomial Model," CRSP working papers 470, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
    14. Drew Creal & Siem Jan Koopman & André Lucas, 2008. "A General Framework for Observation Driven Time-Varying Parameter Models," Tinbergen Institute Discussion Papers 08-108/4, Tinbergen Institute.
    15. Juan Dolado, 2012. "Comments on: Some recent theory for autoregressive count time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 442-446, September.
    16. Georges Dionne & Xiaozhou Zhou, 2020. "The dynamics of ex-ante weighted spread: an empirical analysis," Quantitative Finance, Taylor & Francis Journals, vol. 20(4), pages 593-617, April.
    17. Feigin, Paul D. & Gould, Phillip & Martin, Gael M. & Snyder, Ralph D., 2008. "Feasible parameter regions for alternative discrete state space models," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2963-2970, December.
    18. Konstantinos Fokianos & Benjamin Kedem, 2004. "Partial Likelihood Inference For Time Series Following Generalized Linear Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 173-197, March.
    19. Vurukonda Sathish & Siuli Mukhopadhyay & Rashmi Tiwari, 2022. "Autoregressive and moving average models for zero‐inflated count time series," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(2), pages 190-218, May.

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