IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v44y2023i1p93-124.html
   My bibliography  Save this article

Seasonal count time series

Author

Listed:
  • Jiajie Kong
  • Robert Lund

Abstract

Count time series are widely encountered in practice. As with continuous valued data, many count series have seasonal properties. This article uses a recent advance in stationary count time series to develop a general seasonal count time series modeling paradigm. The model constructed here permits any marginal distribution for the series and the most flexible autocorrelations possible, including those with negative dependence. Likelihood methods of inference are explored. The article first develops the modeling methods, which entail a discrete transformation of a Gaussian process having seasonal dynamics. Properties of this model class are then established and particle filtering likelihood methods of parameter estimation are developed. A simulation study demonstrating the efficacy of the methods is presented and an application to the number of rainy days in successive weeks in Seattle, Washington is given.

Suggested Citation

  • Jiajie Kong & Robert Lund, 2023. "Seasonal count time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(1), pages 93-124, January.
    • Handle: RePEc:bla:jtsera:v:44:y:2023:i:1:p:93-124
    DOI: 10.1111/jtsa.12651
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/jtsa.12651
    Download Restriction: no
    File URL: https://libkey.io/10.1111/jtsa.12651?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. Paul Glasserman & David D. Yao, 1992. "Some Guidelines and Guarantees for Common Random Numbers," Management Science, INFORMS, vol. 38(6), pages 884-908, June.
    2. Shao, Q., 2006. "Mixture periodic autoregressive time series models," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 609-618, March.
    3. Franses, Philip Hans & Paap, Richard, 2004. "Periodic Time Series Models," OUP Catalogue, Oxford University Press, number 9780199242030.
    4. Leda D. Minkova & Edward Omey, 2014. "A New Markov Binomial Distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(13), pages 2674-2688, July.
    5. Robert Lund & I. V. Basawa, 2000. "Recursive Prediction and Likelihood Evaluation for Periodic ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(1), pages 75-93, January.
    6. Mohamed Bentarzi & Wissam Bentarzi, 2017. "Periodic integer-valued bilinear time series model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(3), pages 1184-1201, February.
    7. Nathan L. Kleinman & James C. Spall & Daniel Q. Naiman, 1999. "Simulation-Based Optimization with Stochastic Approximation Using Common Random Numbers," Management Science, INFORMS, vol. 45(11), pages 1570-1578, November.
    8. Aknouche, Abdelhakim & Bentarzi, Wissam & Demouche, Nacer, 2018. "On periodic ergodicity of a general periodic mixed Poisson autoregression," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 15-21.
    9. I. V. Basawa & Robert Lund, 2001. "Large Sample Properties of Parameter Estimates for Periodic ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(6), pages 651-663, November.
    10. Cláudia Santos & Isabel Pereira & Manuel G. Scotto, 2021. "On the theory of periodic multivariate INAR processes," Statistical Papers, Springer, vol. 62(3), pages 1291-1348, June.
    11. Masarotto, Guido & Varin, Cristiano, 2017. "Gaussian Copula Regression in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 77(i08).
    12. Yun Bai & Jian Kang & Peter X.-K. Song, 2014. "Efficient pairwise composite likelihood estimation for spatial-clustered data," Biometrics, The International Biometric Society, vol. 70(3), pages 661-670, September.
    13. Claudia Czado & Tilmann Gneiting & Leonhard Held, 2009. "Predictive Model Assessment for Count Data," Biometrics, The International Biometric Society, vol. 65(4), pages 1254-1261, December.
    14. Hajivassiliou, Vassilis & McFadden, Daniel & Ruud, Paul, 1996. "Simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 85-134.
    15. Richard A. Davis & Konstantinos Fokianos & Scott H. Holan & Harry Joe & James Livsey & Robert Lund & Vladas Pipiras & Nalini Ravishanker, 2021. "Count Time Series: A Methodological Review," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(535), pages 1533-1547, May.
    16. Qin Shao & Robert Lund, 2004. "Computation and Characterization of Autocorrelations and Partial Autocorrelations in Periodic ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(3), pages 359-372, May.
    17. Franses, Philip Hans, 1994. "A multivariate approach to modeling univariate seasonal time series," Journal of Econometrics, Elsevier, vol. 63(1), pages 133-151, July.
    18. QIN SHAO & ROBERT Lund, 2004. "Computation and Characterization of Autocorrelations and Partial Autocorrelations in Periodic ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(3), pages 359-372, May.
    19. Peter Bloomfield & Harry L. Hurd & Robert B. Lund, 1994. "Periodic Correlation In Stratospheric Ozone Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(2), pages 127-150, 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. Younghoon Kim & Zachary F. Fisher & Vladas Pipiras, 2023. "Latent Gaussian dynamic factor modeling and forecasting for multivariate count time series," Papers 2307.10454, arXiv.org.

    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. Roy, Roch & Saidi, Abdessamad, 2008. "Aggregation and systematic sampling of periodic ARMA processes," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4287-4304, May.
    2. Christian Francq & Roch Roy & Abdessamad Saidi, 2011. "Asymptotic Properties of Weighted Least Squares Estimation in Weak PARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(6), pages 699-723, November.
    3. Yorghos Tripodis & Jeremy Penzer, 2009. "Modelling time series with season-dependent autocorrelation structure," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(7), pages 559-574.
    4. T. Manouchehri & A. R. Nematollahi, 2019. "Periodic autoregressive models with closed skew-normal innovations," Computational Statistics, Springer, vol. 34(3), pages 1183-1213, September.
    5. Shao, Q. & Ni, P.P., 2004. "Least-squares estimation and ANOVA for periodic autoregressive time series," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 287-297, September.
    6. Aleksandra Grzesiek & Prashant Giri & S. Sundar & Agnieszka WyŁomańska, 2020. "Measures of Cross‐Dependence for Bidimensional Periodic AR(1) Model with α‐Stable Distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 785-807, November.
    7. Anderson, Paul L. & Kavalieris, Laimonis & Meerschaert, Mark M., 2008. "Innovations algorithm asymptotics for periodically stationary time series with heavy tails," Journal of Multivariate Analysis, Elsevier, vol. 99(1), pages 94-116, January.
    8. Shao, Q., 2006. "Mixture periodic autoregressive time series models," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 609-618, March.
    9. Paul L. Anderson & Farzad Sabzikar & Mark M. Meerschaert, 2021. "Parsimonious time series modeling for high frequency climate data," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 442-470, July.
    10. Amaral, Luiz Felipe & Souza, Reinaldo Castro & Stevenson, Maxwell, 2008. "A smooth transition periodic autoregressive (STPAR) model for short-term load forecasting," International Journal of Forecasting, Elsevier, vol. 24(4), pages 603-615.
    11. Hindrayanto, Irma & Koopman, Siem Jan & Ooms, Marius, 2010. "Exact maximum likelihood estimation for non-stationary periodic time series models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2641-2654, November.
    12. Philip Hans Franses & Richard Paap, 2011. "Random‐coefficient periodic autoregressions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(1), pages 101-115, February.
    13. Soumya Das & Marc G. Genton & Yasser M. Alshehri & Georgiy L. Stenchikov, 2021. "A cyclostationary model for temporal forecasting and simulation of solar global horizontal irradiance," Environmetrics, John Wiley & Sons, Ltd., vol. 32(8), December.
    14. Basawa, I. V. & Lund, Robert & Shao, Qin, 2004. "First-order seasonal autoregressive processes with periodically varying parameters," Statistics & Probability Letters, Elsevier, vol. 67(4), pages 299-306, May.
    15. Politis, Dimitris, 2016. "HEGY test under seasonal heterogeneity," University of California at San Diego, Economics Working Paper Series qt2q4054kf, Department of Economics, UC San Diego.
    16. Domenico Cucina & Manuel Rizzo & Eugen Ursu, 2018. "Identification of multiregime periodic autotregressive models by genetic algorithms," Post-Print hal-03187870, HAL.
    17. Haldrup, Niels & Hylleberg, Svend & Pons, Gabriel & Sanso, Andreu, 2007. "Common Periodic Correlation Features and the Interaction of Stocks and Flows in Daily Airport Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 21-32, January.
    18. 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).
    19. A.S.M. Arroyo & A. de Juan Fern¨¢ndez, 2014. "Split-then-Combine Method for out-of-sample Combinations of Forecasts," Journal of Business Administration Research, Journal of Business Administration Research, Sciedu Press, vol. 3(1), pages 19-37, April.
    20. Tomás Barrio & Mariam Camarero & Cecilio Tamarit, 2019. "Testing for Periodic Integration with a Changing Mean," Computational Economics, Springer;Society for Computational Economics, vol. 54(1), pages 45-75, June.

    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:44:y:2023:i:1:p:93-124. 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.