IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2202.02029.html
   My bibliography  Save this paper

First-order integer-valued autoregressive processes with Generalized Katz innovations

Author

Listed:
  • Federico Bassetti
  • Giulia Carallo
  • Roberto Casarin

Abstract

A new integer-valued autoregressive process (INAR) with Generalised Lagrangian Katz (GLK) innovations is defined. We show that our GLK-INAR process is stationary, discrete semi-self-decomposable, infinite divisible, and provides a flexible modelling framework for count data allowing for under- and over-dispersion, asymmetry, and excess of kurtosis. A Bayesian inference framework and an efficient posterior approximation procedure based on Markov Chain Monte Carlo are provided. The proposed model family is applied to a Google Trend dataset which proxies the public concern about climate change around the world. The empirical results provide new evidence of heterogeneity across countries and keywords in the persistence, uncertainty, and long-run public awareness level.

Suggested Citation

  • Federico Bassetti & Giulia Carallo & Roberto Casarin, 2022. "First-order integer-valued autoregressive processes with Generalized Katz innovations," Papers 2202.02029, arXiv.org.
    • Handle: RePEc:arx:papers:2202.02029
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2202.02029
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Du Jin‐Guan & Li Yuan, 1991. "THE INTEGER‐VALUED AUTOREGRESSIVE (INAR(p)) MODEL," Journal of Time Series Analysis, Wiley Blackwell, vol. 12(2), pages 129-142, March.
    2. Hee-Young Kim & Yousung Park, 2008. "A non-stationary integer-valued autoregressive model," Statistical Papers, Springer, vol. 49(3), pages 485-502, July.
    3. Frondel, Manuel & Simora, Michael & Sommer, Stephan, 2017. "Risk Perception of Climate Change: Empirical Evidence for Germany," Ecological Economics, Elsevier, vol. 137(C), pages 173-183.
    4. Roman Liesenfeld & Ingmar Nolte & Winfried Pohlmeier, 2008. "Modelling financial transaction price movements: a dynamic integer count data model," Studies in Empirical Economics, in: Luc Bauwens & Winfried Pohlmeier & David Veredas (ed.), High Frequency Financial Econometrics, pages 167-197, Springer.
    5. Caterina Schiavoni & Franz Palm & Stephan Smeekes & Jan van den Brakel, 2021. "A dynamic factor model approach to incorporate Big Data in state space models for official statistics," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(1), pages 324-353, January.
    6. Brendan P. M. McCabe & Christopher L. Skeels, 2020. "Distributions You Can Count On …But What’s the Point?," Econometrics, MDPI, vol. 8(1), pages 1-36, March.
    7. Tina Hviid Rydberg & Neil Shephard, 2003. "Dynamics of Trade-by-Trade Price Movements: Decomposition and Models," Journal of Financial Econometrics, Oxford University Press, vol. 1(1), pages 2-25.
    8. 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.
    9. Ziegler, Andreas, 2017. "Political orientation, environmental values, and climate change beliefs and attitudes: An empirical cross country analysis," Energy Economics, Elsevier, vol. 63(C), pages 144-153.
    10. Hyunyoung Choi & Hal Varian, 2012. "Predicting the Present with Google Trends," The Economic Record, The Economic Society of Australia, vol. 88(s1), pages 2-9, June.
    11. Lindsay R. Berry & Mike West, 2020. "Bayesian Forecasting of Many Count-Valued Time Series," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(4), pages 872-887, October.
    12. Dingdong Yi & Shaoyang Ning & Chia-Jung Chang & S. C. Kou, 2021. "Forecasting Unemployment Using Internet Search Data via PRISM," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1662-1673, October.
    13. Ardia David & Bluteau Keven & Hoogerheide Lennart F., 2018. "Methods for Computing Numerical Standard Errors: Review and Application to Value-at-Risk Estimation," Journal of Time Series Econometrics, De Gruyter, vol. 10(2), pages 1-9, July.
    14. Yu, Lean & Zhao, Yaqing & Tang, Ling & Yang, Zebin, 2019. "Online big data-driven oil consumption forecasting with Google trends," International Journal of Forecasting, Elsevier, vol. 35(1), pages 213-223.
    15. M. A. Al‐Osh & A. A. Alzaid, 1987. "First‐Order Integer‐Valued Autoregressive (Inar(1)) Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(3), pages 261-275, May.
    16. 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.
    17. McCabe, B.P.M. & Martin, G.M., 2005. "Bayesian predictions of low count time series," International Journal of Forecasting, Elsevier, vol. 21(2), pages 315-330.
    18. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    19. 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.
    20. Peter Neal & T. Subba Rao, 2007. "MCMC for Integer‐Valued ARMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(1), pages 92-110, January.
    21. Cathy W. S. Chen & Sangyeol Lee, 2017. "Bayesian causality test for integer-valued time series models with applications to climate and crime data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(4), pages 797-814, August.
    22. R. Freeland, 2010. "True integer value time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(3), pages 217-229, September.
    23. Fahad, Shah & Wang, Jianling, 2018. "Farmers’ risk perception, vulnerability, and adaptation to climate change in rural Pakistan," Land Use Policy, Elsevier, vol. 79(C), pages 301-309.
    24. Golnaz Shahtahmassebi & Rana Moyeed, 2016. "An application of the generalized Poisson difference distribution to the Bayesian modelling of football scores," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(3), pages 260-273, August.
    25. Nadjib Bouzar, 2008. "Semi-self-decomposable distributions on Z +," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(4), pages 901-917, December.
    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. Giulia Carallo & Roberto Casarin & Christian P. Robert, 2020. "Generalized Poisson Difference Autoregressive Processes," Papers 2002.04470, arXiv.org.
    2. Yang, Kai & Yu, Xinyang & Zhang, Qingqing & Dong, Xiaogang, 2022. "On MCMC sampling in self-exciting integer-valued threshold time series models," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    3. Xinyang Wang & Dehui Wang & Kai Yang, 2021. "Integer-valued time series model order shrinkage and selection via penalized quasi-likelihood approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 713-750, July.
    4. 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.
    5. Chen, Cathy W.S. & Liu, Feng-Chi & Pingal, Aljo Clair, 2023. "Integer-valued transfer function models for counts that show zero inflation," Statistics & Probability Letters, Elsevier, vol. 193(C).
    6. Cathy W. S. Chen & Sangyeol Lee & K. Khamthong, 2021. "Bayesian inference of nonlinear hysteretic integer-valued GARCH models for disease counts," Computational Statistics, Springer, vol. 36(1), pages 261-281, March.
    7. Trojan, Sebastian, 2014. "Modeling Intraday Stochastic Volatility and Conditional Duration Contemporaneously with Regime Shifts," Economics Working Paper Series 1425, University of St. Gallen, School of Economics and Political Science.
    8. Zhongchen Song & Tom Coupé, 2023. "Predicting Chinese consumption series with Baidu," Journal of Chinese Economic and Business Studies, Taylor & Francis Journals, vol. 21(3), pages 429-463, July.
    9. Schaer, Oliver & Kourentzes, Nikolaos & Fildes, Robert, 2019. "Demand forecasting with user-generated online information," International Journal of Forecasting, Elsevier, vol. 35(1), pages 197-212.
    10. Kai Yang & Han Li & Dehui Wang & Chenhui Zhang, 2021. "Random coefficients integer-valued threshold autoregressive processes driven by logistic regression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 533-557, December.
    11. Leopoldo Catania & Roberto Di Mari & Paolo Santucci de Magistris, 2019. "Dynamic discrete mixtures for high frequency prices," Discussion Papers 19/05, University of Nottingham, Granger Centre for Time Series Econometrics.
    12. Kachour Maher & Bakouch Hassan S. & Mohammadi Zohreh, 2023. "A New INAR(1) Model for ℤ-Valued Time Series Using the Relative Binomial Thinning Operator," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 243(2), pages 125-152, April.
    13. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    14. Timothy Christensen & Stan Hurn & Kenneth Lindsay, 2009. "It Never Rains but it Pours: Modeling the Persistence of Spikes in Electricity Prices," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1), pages 25-48.
    15. 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.
    16. Daniel Borup & Erik Christian Montes Schütte, 2022. "In Search of a Job: Forecasting Employment Growth Using Google Trends," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 186-200, January.
    17. Francesco Bravo, 2011. "Comment on: Subsampling weakly dependent time series and application to extremes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 483-486, November.
    18. Dean Fantazzini & Julia Pushchelenko & Alexey Mironenkov & Alexey Kurbatskii, 2021. "Forecasting Internal Migration in Russia Using Google Trends: Evidence from Moscow and Saint Petersburg," Forecasting, MDPI, vol. 3(4), pages 1-30, October.
    19. Jung, Robert C. & Kukuk, Martin & Liesenfeld, Roman, 2006. "Time series of count data: modeling, estimation and diagnostics," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2350-2364, December.
    20. 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).

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2202.02029. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.