IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v119y2016icp264-272.html
   My bibliography  Save this article

A geometric time series model with inflated-parameter Bernoulli counting series

Author

Listed:
  • Borges, Patrick
  • Molinares, Fabio Fajardo
  • Bourguignon, Marcelo

Abstract

In this paper, we propose a new stationary first-order non-negative integer valued autoregressive [INAR(1)] process with geometric marginals based on a modified version of the binomial thinning operator. This new process will enable one to tackle the problem of overdispersion inherent in the analysis of integer-valued time series data that may arise due to the presence of some correlation between underlying events, heterogeneity of the population, excess to zeros, among others. In addition, it includes as special cases the geometric INAR(1) [GINAR(1)] (Alzaid and Al-Osh, 1988) and new geometric [NGINAR(1)] (Ristić et al., 2009) processes, making it be very useful in discriminating between nested models. The innovation structure of the new process is very simple. The main properties of the process are derived, such as conditional distribution, autocorrelation structure, innovation structure and jumps. The method of conditional maximum likelihood is used for estimating the process parameters. Some numerical results of the estimators are presented with a brief discussion. In order to illustrate the potential for practice of our process we apply it to a real data set.

Suggested Citation

  • Borges, Patrick & Molinares, Fabio Fajardo & Bourguignon, Marcelo, 2016. "A geometric time series model with inflated-parameter Bernoulli counting series," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 264-272.
    • Handle: RePEc:eee:stapro:v:119:y:2016:i:c:p:264-272
    DOI: 10.1016/j.spl.2016.08.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715215304399
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2016.08.012?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. Miroslav M. Ristić & Aleksandar S. Nastić, 2012. "A mixed INAR(p) model," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(6), pages 903-915, November.
    2. Schweer, Sebastian & Weiß, Christian H., 2014. "Compound Poisson INAR(1) processes: Stochastic properties and testing for overdispersion," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 267-284.
    3. M. Kachour & J. F. Yao, 2009. "First‐order rounded integer‐valued autoregressive (RINAR(1)) process," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(4), pages 417-448, July.
    4. R. K. Freeland & B. P. M. McCabe, 2004. "Analysis of low count time series data by poisson autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 701-722, September.
    5. Hyndman, Rob J. & Koehler, Anne B., 2006. "Another look at measures of forecast accuracy," International Journal of Forecasting, Elsevier, vol. 22(4), pages 679-688.
    6. Miroslav M. Ristić & Aleksandar S. Nastić & Ana V. Miletić Ilić, 2013. "A geometric time series model with dependent Bernoulli counting series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 466-476, July.
    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. Shirozhan, M. & Bakouch, Hassan S. & Mohammadpour, M., 2023. "A flexible INAR(1) time series model with dependent zero-inflated count series and medical contagious cases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 216-230.
    2. Nisreen Shamma & Mehrnaz Mohammadpour & Masoumeh Shirozhan, 2020. "A time series model based on dependent zero inflated counting series," Computational Statistics, Springer, vol. 35(4), pages 1737-1757, December.
    3. Masoomeh Forughi & Zohreh Shishebor & Atefeh Zamani, 2022. "Portmanteau tests for generalized integer-valued autoregressive time series models," Statistical Papers, Springer, vol. 63(4), pages 1163-1185, August.

    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. Wagner Barreto-Souza, 2015. "Zero-Modified Geometric INAR(1) Process for Modelling Count Time Series with Deflation or Inflation of Zeros," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 839-852, November.
    2. Marcelo Bourguignon, 2016. "Poisson–geometric INAR(1) process for modeling count time series with overdispersion," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(3), pages 176-192, August.
    3. Wagner Barreto-Souza, 2019. "Mixed Poisson INAR(1) processes," Statistical Papers, Springer, vol. 60(6), pages 2119-2139, December.
    4. José M. R. Murteira & Mário A. G. Augusto, 2017. "Hurdle models of repayment behaviour in personal loan contracts," Empirical Economics, Springer, vol. 53(2), pages 641-667, September.
    5. Layth C. Alwan & Christian H. Weiß, 2017. "INAR implementation of newsvendor model for serially dependent demand counts," International Journal of Production Research, Taylor & Francis Journals, vol. 55(4), pages 1085-1099, February.
    6. Raju Maiti & Atanu Biswas & Samarjit Das, 2016. "Coherent forecasting for count time series using Box–Jenkins's AR(p) model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(2), pages 123-145, May.
    7. 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.
    8. Wagner Barreto‐Souza & Hernando Ombao, 2022. "The negative binomial process: A tractable model with composite likelihood‐based inference," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 568-592, June.
    9. Manik Awale & N. Balakrishna & T. V. Ramanathan, 2019. "Testing the constancy of the thinning parameter in a random coefficient integer autoregressive model," Statistical Papers, Springer, vol. 60(5), pages 1515-1539, October.
    10. Bisaglia, Luisa & Canale, Antonio, 2016. "Bayesian nonparametric forecasting for INAR models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 70-78.
    11. Miroslav M. Ristić & Aleksandar S. Nastić & Ana V. Miletić Ilić, 2013. "A geometric time series model with dependent Bernoulli counting series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 466-476, July.
    12. repec:prg:jnlcfu:v:2022:y:2022:i:1:id:572 is not listed on IDEAS
    13. Chang, Andrew C. & Hanson, Tyler J., 2016. "The accuracy of forecasts prepared for the Federal Open Market Committee," Journal of Economics and Business, Elsevier, vol. 83(C), pages 23-43.
    14. Frank, Johannes, 2023. "Forecasting realized volatility in turbulent times using temporal fusion transformers," FAU Discussion Papers in Economics 03/2023, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    15. Kourentzes, Nikolaos & Petropoulos, Fotios & Trapero, Juan R., 2014. "Improving forecasting by estimating time series structural components across multiple frequencies," International Journal of Forecasting, Elsevier, vol. 30(2), pages 291-302.
    16. Paulo Júlio & Pedro M. Esperança, 2012. "Evaluating the forecast quality of GDP components: An application to G7," GEE Papers 0047, Gabinete de Estratégia e Estudos, Ministério da Economia, revised Apr 2012.
    17. Cameron Roach & Rob Hyndman & Souhaib Ben Taieb, 2021. "Non‐linear mixed‐effects models for time series forecasting of smart meter demand," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(6), pages 1118-1130, September.
    18. Alysha M De Livera, 2010. "Automatic forecasting with a modified exponential smoothing state space framework," Monash Econometrics and Business Statistics Working Papers 10/10, Monash University, Department of Econometrics and Business Statistics.
    19. Nikitopoulos, Christina Sklibosios & Thomas, Alice Carole & Wang, Jianxin, 2023. "The economic impact of daily volatility persistence on energy markets," Journal of Commodity Markets, Elsevier, vol. 30(C).
    20. I. Yu. Zolotova & V. V. Dvorkin, 2017. "Short-term forecasting of prices for the Russian wholesale electricity market based on neural networks," Studies on Russian Economic Development, Springer, vol. 28(6), pages 608-615, November.
    21. Döpke, Jörg & Fritsche, Ulrich & Müller, Karsten, 2019. "Has macroeconomic forecasting changed after the Great Recession? Panel-based evidence on forecast accuracy and forecaster behavior from Germany," Journal of Macroeconomics, Elsevier, vol. 62(C).

    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:stapro:v:119:y:2016:i:c:p:264-272. 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.