IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v43y2022i2p285-311.html
   My bibliography  Save this article

Generalized binary vector autoregressive processes

Author

Listed:
  • Carsten Jentsch
  • Lena Reichmann

Abstract

Vector‐valued‐60 extensions of univariate generalized binary auto‐regressive (gbAR) processes are proposed that enable the joint modeling of serial and cross‐sectional‐50 dependence of multi‐variate binary data. The resulting class of generalized binary vector auto‐regressive (gbVAR) models is parsimonious, nicely interpretable and allows also to model negative dependence. We provide stationarity conditions and derive moving‐average‐type representations that allow to prove geometric mixing properties. Furthermore, we derive general stochastic properties of gbVAR processes, including formulae for transition probabilities. In particular, classical Yule–Walker equations hold that facilitate parameter estimation in gbVAR models. In simulations, we investigate the estimation performance, and for illustration, we apply gbVAR models to particulate matter (PM10, ‘fine dust’) alarm data observed at six monitoring stations in Stuttgart, Germany.

Suggested Citation

  • Carsten Jentsch & Lena Reichmann, 2022. "Generalized binary vector autoregressive processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 285-311, March.
  • Handle: RePEc:bla:jtsera:v:43:y:2022:i:2:p:285-311
    DOI: 10.1111/jtsa.12614
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/jtsa.12614
    Download Restriction: no

    File URL: https://libkey.io/10.1111/jtsa.12614?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
    ---><---

    References listed on IDEAS

    as
    1. Bertrand Candelon & Elena-Ivona Dumitrescu & Christophe Hurlin & Franz C. Palm, 2013. "Multivariate Dynamic Probit Models: An Application to Financial Crises Mutation," Advances in Econometrics, in: VAR Models in Macroeconomics – New Developments and Applications: Essays in Honor of Christopher A. Sims, volume 32, pages 395-427, Emerald Group Publishing Limited.
    2. Bo E. Honoré & Ekaterini Kyriazidou, 2019. "Identification in Binary Response Panel Data Models: Is Point-Identification More Common Than We Thought?," Annals of Economics and Statistics, GENES, issue 134, pages 207-226.
    3. Carsten Jentsch & Lena Reichmann, 2019. "Generalized Binary Time Series Models," Econometrics, MDPI, vol. 7(4), pages 1-26, December.
    4. P. A. Jacobs & P. A. W. Lewis, 1983. "Stationary Discrete Autoregressive‐Moving Average Time Series Generated By Mixtures," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(1), pages 19-36, January.
    5. Christian Weiß & Rainer Göb, 2008. "Measuring serial dependence in categorical time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(1), pages 71-89, February.
    Full references (including those not matched with items on IDEAS)

    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. Atanu Biswas & Maria Carmen Pardo & Apratim Guha, 2014. "Auto-association measures for stationary time series of categorical data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 487-514, September.
    2. Raju Maiti & Atanu Biswas, 2015. "Coherent forecasting for stationary time series of discrete data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(3), pages 337-365, July.
    3. Christian H. Weiß, 2019. "Measures of Dispersion and Serial Dependence in Categorical Time Series," Econometrics, MDPI, vol. 7(2), pages 1-23, April.
    4. Carsten Jentsch & Lena Reichmann, 2019. "Generalized Binary Time Series Models," Econometrics, MDPI, vol. 7(4), pages 1-26, December.
    5. A. M. M. Shahiduzzaman Quoreshi & Reaz Uddin & Naushad Mamode Khan, 2019. "Quasi-Maximum Likelihood Estimation for Long Memory Stock Transaction Data—Under Conditional Heteroskedasticity Framework," JRFM, MDPI, vol. 12(2), pages 1-13, April.
    6. Tobias A. Möller & Christian H. Weiß, 2020. "Generalized discrete autoregressive moving‐average models," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(4), pages 641-659, July.
    7. Song‐Hee Kim & Ward Whitt, 2014. "Choosing arrival process models for service systems: Tests of a nonhomogeneous Poisson process," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(1), pages 66-90, February.
    8. Damian Eduardo Taranto & Giacomo Bormetti & Fabrizio Lillo, 2014. "The adaptive nature of liquidity taking in limit order books," Papers 1403.0842, arXiv.org, revised Apr 2014.
    9. William W. Chow & Michael K. Fung, 2021. "The effects of macroprudential policy on Hong Kong’s housing market: a multivariate ordered probit-augmented vector autoregressive approach," Empirical Economics, Springer, vol. 60(2), pages 633-660, February.
    10. Maixé-Altés, J. Carles & Iglesias, Emma M., 2015. "Banking, Currency, Stock Market and Debt Crises: Revisiting Reinhart & Rogoff Debt Analysis in Spain, 1850-1995," MPRA Paper 68199, University Library of Munich, Germany.
    11. Guodong Pang & Ward Whitt, 2012. "The Impact of Dependent Service Times on Large-Scale Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 14(2), pages 262-278, April.
    12. Maria Eduarda Da Silva & Vera Lúcia Oliveira, 2004. "Difference Equations for the Higher‐Order Moments and Cumulants of the INAR(1) Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(3), pages 317-333, May.
    13. Bo E. Honoré & Martin Weidner, 2021. "Moment Conditions for Dynamic Panel Logit Models with Fixed Effects," Working Papers 2021-79, Princeton University. Economics Department..
    14. Candelon, Bertrand & Hasse, Jean-Baptiste, 2023. "Testing for causality between climate policies and carbon emissions reduction," Finance Research Letters, Elsevier, vol. 55(PA).
    15. Chris Muris & Pedro Raposo & Sotiris Vandoros, 2020. "A dynamic ordered logit model with fixed effects," Papers 2008.05517, arXiv.org.
    16. Manner, Hans & Türk, Dennis & Eichler, Michael, 2016. "Modeling and forecasting multivariate electricity price spikes," Energy Economics, Elsevier, vol. 60(C), pages 255-265.
    17. Barrera, Carlos, 2014. "La relación entre los ciclos discretos en la inflación y el crecimiento: Perú 1993 - 2012," Working Papers 2014-024, Banco Central de Reserva del Perú.
    18. Kosmidis, Kosmas & Hütt, Marc-Thorsten, 2023. "DNA visibility graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    19. Khan, S. & Ponomareva, M. & Tamer, E., 2023. "Identification of dynamic binary response models," Journal of Econometrics, Elsevier, vol. 237(1).
    20. Kharin, Yuriy & Voloshko, Valeriy, 2021. "Robust estimation for Binomial conditionally nonlinear autoregressive time series based on multivariate conditional frequencies," Journal of Multivariate Analysis, Elsevier, vol. 185(C).

    More about this item

    Statistics

    Access and download statistics

    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:bla:jtsera:v:43:y:2022:i:2:p:285-311. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.