IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v125y2014icp233-251.html
   My bibliography  Save this article

Bivariate binomial autoregressive models

Author

Listed:
  • Scotto, Manuel G.
  • Weiß, Christian H.
  • Silva, Maria Eduarda
  • Pereira, Isabel

Abstract

This paper introduces new classes of bivariate time series models being useful to fit count data time series with a finite range of counts. Motivation comes mainly from the comparison of schemes for monitoring tourism demand, stock data, production and environmental processes. All models are based on the bivariate binomial distribution of Type II. First, a new family of bivariate integer-valued GARCH models is proposed. Then, a new bivariate thinning operation is introduced and explained in detail. The new thinning operation has a number of advantages including the fact that marginally it behaves as the usual binomial thinning operation and also that allows for both positive and negative cross-correlations. Based upon this new thinning operation, a bivariate extension of the binomial autoregressive model of order one is introduced. Basic probabilistic and statistical properties of the model are discussed. Parameter estimation and forecasting are also covered. The performance of these models is illustrated through an empirical application to a set of rainy days time series collected from 2000 up to 2010 in the German cities of Bremen and Cuxhaven.

Suggested Citation

  • Scotto, Manuel G. & Weiß, Christian H. & Silva, Maria Eduarda & Pereira, Isabel, 2014. "Bivariate binomial autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 233-251.
    • Handle: RePEc:eee:jmvana:v:125:y:2014:i:c:p:233-251
    DOI: 10.1016/j.jmva.2013.12.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X14000086
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2013.12.014?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fokianos, Konstantinos & Rahbek, Anders & Tjøstheim, Dag, 2009. "Poisson Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1430-1439.
    2. Brännäs, Kurt & Quoreshi, Shahiduzzaman, 2004. "Integer-Valued Moving Average Modelling of the Number of Transactions in Stocks," Umeå Economic Studies 637, Umeå University, Department of Economics.
    3. 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.
    4. Freeland, R. K. & McCabe, B. P. M., 2004. "Forecasting discrete valued low count time series," International Journal of Forecasting, Elsevier, vol. 20(3), pages 427-434.
    5. Jonas Andersson & Dimitris Karlis, 2010. "Treating missing values in INAR(1) models: An application to syndromic surveillance data," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(1), pages 12-19, January.
    6. Yunwei Cui & Robert Lund, 2009. "A new look at time series of counts," Biometrika, Biometrika Trust, vol. 96(4), pages 781-792.
    7. Zhu, Fukang & Wang, Dehui, 2010. "Diagnostic checking integer-valued ARCH(p) models using conditional residual autocorrelations," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 496-508, February.
    8. Zhou, J. & Basawa, I.V., 2005. "Least-squares estimation for bifurcating autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 77-88, August.
    9. René Ferland & Alain Latour & Driss Oraichi, 2006. "Integer‐Valued GARCH Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 923-942, November.
    10. Biswas, Atanu & Hwang, Jing-Shiang, 2002. "A new bivariate binomial distribution," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 231-240, November.
    11. Christian H. Weiß & Philip K. Pollett, 2012. "Chain Binomial Models and Binomial Autoregressive Processes," Biometrics, The International Biometric Society, vol. 68(3), pages 815-824, September.
    12. Quoreshi, Shahiduzzaman, 2005. "Bivariate Time Series Modelling of Financial Count Data," Umeå Economic Studies 655, Umeå University, Department of Economics.
    13. Dag Tjøstheim, 2012. "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 413-438, September.
    14. Christian Weiß, 2009. "Modelling time series of counts with overdispersion," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(4), pages 507-519, November.
    15. Cui, Yunwei & Lund, Robert, 2010. "Inference in binomial models," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1985-1990, December.
    16. Alexandra M. Schmidt & João Batista M. Pereira, 2011. "Modelling Time Series of Counts in Epidemiology," International Statistical Review, International Statistical Institute, vol. 79(1), pages 48-69, April.
    17. Heinen, Andreas & Rengifo, Erick, 2007. "Multivariate autoregressive modeling of time series count data using copulas," Journal of Empirical Finance, Elsevier, vol. 14(4), pages 564-583, September.
    18. Konstantinos Fokianos & Dag Tjøstheim, 2012. "Nonlinear Poisson autoregression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(6), pages 1205-1225, December.
    19. Christian Weiss, 2009. "Monitoring correlated processes with binomial marginals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(4), pages 399-414.
    20. Fukang Zhu & Dehui Wang, 2011. "Estimation and testing for a Poisson autoregressive model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(2), pages 211-230, March.
    21. Xanthi Pedeli & Dimitris Karlis, 2013. "On composite likelihood estimation of a multivariate INAR(1) model," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(2), pages 206-220, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chen, Cathy W.S. & Chen, Chun-Shu & Hsiung, Mo-Hua, 2023. "Bayesian modeling of spatial integer-valued time series," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).
    2. Darolles, Serge & Fol, Gaëlle Le & Lu, Yang & Sun, Ran, 2019. "Bivariate integer-autoregressive process with an application to mutual fund flows," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 181-203.
    3. Huaping Chen & Fukang Zhu & Xiufang Liu, 2022. "A New Bivariate INAR(1) Model with Time-Dependent Innovation Vectors," Stats, MDPI, vol. 5(3), pages 1-22, August.
    4. Kai Yang & Yiwei Zhao & Han Li & Dehui Wang, 2023. "On bivariate threshold Poisson integer-valued autoregressive processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(8), pages 931-963, November.
    5. Yao Kang & Dehui Wang & Kai Yang, 2021. "A new INAR(1) process with bounded support for counts showing equidispersion, underdispersion and overdispersion," Statistical Papers, Springer, vol. 62(2), pages 745-767, April.
    6. Yao Kang & Shuhui Wang & Dehui Wang & Fukang Zhu, 2023. "Analysis of zero-and-one inflated bounded count time series with applications to climate and crime data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 34-73, March.
    7. Predrag M. Popović & Hassan S. Bakouch, 2020. "A bivariate integer-valued bilinear autoregressive model with random coefficients," Statistical Papers, Springer, vol. 61(5), pages 1819-1840, October.
    8. Qingchun Zhang & Dehui Wang & Xiaodong Fan, 2020. "A negative binomial thinning‐based bivariate INAR(1) process," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(4), pages 517-537, November.
    9. Luiza S. C. Piancastelli & Wagner Barreto‐Souza & Hernando Ombao, 2023. "Flexible bivariate INGARCH process with a broad range of contemporaneous correlation," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(2), pages 206-222, March.
    10. Tobias A. Möller & Maria Eduarda Silva & Christian H. Weiß & Manuel G. Scotto & Isabel Pereira, 2016. "Self-exciting threshold binomial autoregressive processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 369-400, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Christian H. Weiß & Esmeralda Gonçalves & Nazaré Mendes Lopes, 2017. "Testing the compounding structure of the CP-INARCH model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(5), pages 571-603, July.
    2. Christian H. Weiß & Sebastian Schweer, 2015. "Detecting overdispersion in INARCH(1) processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(3), pages 281-297, August.
    3. Jiwon Kang & Sangyeol Lee, 2014. "Parameter Change Test for Poisson Autoregressive Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1136-1152, December.
    4. Weiß, Christian H., 2010. "INARCH(1) processes: Higher-order moments and jumps," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1771-1780, December.
    5. Fukang Zhu & Lei Shi & Shuangzhe Liu, 2015. "Influence diagnostics in log-linear integer-valued GARCH models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(3), pages 311-335, July.
    6. Šárka Hudecová & Marie Hušková & Simos G. Meintanis, 2021. "Goodness–of–Fit Tests for Bivariate Time Series of Counts," Econometrics, MDPI, vol. 9(1), pages 1-20, March.
    7. Huiyu Mao & Fukang Zhu & Yan Cui, 2020. "A generalized mixture integer-valued GARCH model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 527-552, September.
    8. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2020. "On an integer-valued stochastic intensity model for time series of counts," MPRA Paper 105406, University Library of Munich, Germany.
    9. Fokianos, Konstantinos & Fried, Roland & Kharin, Yuriy & Voloshko, Valeriy, 2022. "Statistical analysis of multivariate discrete-valued time series," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    10. William Kengne & Isidore S. Ngongo, 2022. "Inference for nonstationary time series of counts with application to change-point problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 801-835, August.
    11. Dag Tjøstheim, 2012. "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 413-438, September.
    12. Yan Cui & Fukang Zhu, 2018. "A new bivariate integer-valued GARCH model allowing for negative cross-correlation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 428-452, June.
    13. Xu, Hai-Yan & Xie, Min & Goh, Thong Ngee & Fu, Xiuju, 2012. "A model for integer-valued time series with conditional overdispersion," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4229-4242.
    14. Chen, Cathy W.S. & Lee, Sangyeol, 2016. "Generalized Poisson autoregressive models for time series of counts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 51-67.
    15. Christian Weiß & Hee-Young Kim, 2013. "Parameter estimation for binomial AR(1) models with applications in finance and industry," Statistical Papers, Springer, vol. 54(3), pages 563-590, August.
    16. Axel Groß‐KlußMann & Nikolaus Hautsch, 2013. "Predicting Bid–Ask Spreads Using Long‐Memory Autoregressive Conditional Poisson Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(8), pages 724-742, December.
    17. Kirchner, Matthias & Torrisi, Giovanni Luca, 2023. "Fluctuations and precise deviations of cumulative INAR time series," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 1-32.
    18. Li, Qi & Lian, Heng & Zhu, Fukang, 2016. "Robust closed-form estimators for the integer-valued GARCH (1,1) model," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 209-225.
    19. Christian H. Weiß, 2018. "Goodness-of-fit testing of a count time series’ marginal distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(6), pages 619-651, August.
    20. Mamadou Lamine Diop & William Kengne, 2017. "Testing Parameter Change in General Integer-Valued Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 880-894, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:125:y:2014:i:c:p:233-251. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.