Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter September 13, 2021

Forecasting transaction counts with integer-valued GARCH models

  • Abdelhakim Aknouche , Bader S. Almohaimeed and Stefanos Dimitrakopoulos EMAIL logo

Abstract

Using numerous transaction data on the number of stock trades, we conduct a forecasting exercise with INGARCH models, governed by various conditional distributions; the Poisson, the linear and quadratic negative binomial, the double Poisson and the generalized Poisson. The model parameters are estimated with efficient Markov Chain Monte Carlo methods, while forecast evaluation is done by calculating point and density forecasts.


Corresponding author: Stefanos Dimitrakopoulos, Economics Division, Leeds University Business School, University of Leeds, LS2 9JT, Leeds, UK, E-mail:

Acknowledgement

All computations have been performed in the Advanced Research Computing (ARC) environment at the University of Leeds.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

Ahmad, A., and C. Francq. 2016. “Poisson QMLE of Count Time Series Models.” Journal of Time Series Analysis 37 (3): 291–314. https://doi.org/10.1111/jtsa.12167.Search in Google Scholar

Aknouche, A., S. Bendjeddou, and N. Touche. 2018. “Negative Binomial Quasi-Likelihood Inference for General Integer-Valued Time Series Models.” Journal of Time Series Analysis 39 (2): 192–211. https://doi.org/10.1111/jtsa.12277.Search in Google Scholar

Aknouche, A., and C. Francq. 2021. “Count and Duration Time Series with Equal Conditional Stochastic and Mean Orders.” Econometric Theory 37 (2): 248–80. https://doi.org/10.1017/s0266466620000134.Search in Google Scholar

Atchadé, Y. F. 2006. “An Adaptive Version for the Metropolis Adjusted Langevin Algorithm with a Truncated Drift.” Methodology and Computing in Applied Probability 8: 235–54. https://doi.org/10.1007/s11009-006-8550-0.Search in Google Scholar

Berry, L., and M. West. 2020. “Bayesian Forecasting of Many Count-Valued Time Series.” Journal of Business & Economic Statistics 38 (4): 872–87. https://doi.org/10.1080/07350015.2019.1604372.Search in Google Scholar

Cameron, A., and P. Trivedi. 2013. Regression Analysis of Count Data. Cambridge: University Press.10.1017/CBO9781139013567Search in Google Scholar

Chen, C. W. S., M. So, J. C. Li, and S. Sriboonchitta. 2016. “Autoregressive Conditional Negative Binomial Model Applied to Over-dispersed Time Series of Counts.” Statistical Methodology 31: 73–90. https://doi.org/10.1016/j.stamet.2016.02.001.Search in Google Scholar

Chib, S. 2001. “Markov Chain Monte Carlo Methods: Computation and Inference.” In Handbook of Econometrics, edited by J. J. Heckman, and E. V. Leamer, 3569–649. Amsterdam: North-Holland.10.1016/S1573-4412(01)05010-3Search in Google Scholar

Christou, V., and K. Fokianos. 2014. “Quasi-Likelihood Inference for Negative Binomial Time Series Models.” Journal of Time Series Analysis 35 (1): 55–78. https://doi.org/10.1111/jtsa.12050.Search in Google Scholar

Davis, R. A., and H. Liu. 2016. “Theory and Inference for a Class of Observation-Driven Models with Application to Time Series of Counts.” Statistica Sinica 26 (4): 1673–707.Search in Google Scholar

Doukhan, P., K. Fokianos, and D. Tjøstheim. 2012. “On Weak Dependence Conditions for Poisson Autoregressions.” Statistics & Probability Letters 82 (5): 942–8. https://doi.org/10.1016/j.spl.2012.01.015.Search in Google Scholar

Ferland, R., A. Latour, and D. Oraichi. 2006. “Integer-Valued GARCH Process.” Journal of Time Series Analysis 27 (6): 923–42. https://doi.org/10.1111/j.1467-9892.2006.00496.x.Search in Google Scholar

Fokianos, K., A. Rahbek, and D. Tjøstheim. 2009. “Poisson Autoregression.” Journal of the American Statistical Association 140 (488): 1430–9. https://doi.org/10.1198/jasa.2009.tm08270.Search in Google Scholar

Geweke, J. 1992. “Evaluating the Accuracy of Sampling-Based Approaches to the Calculation of Posterior Moments.” In Bayesian Statistics 4, edited by J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, 641–9. Oxford: Clarendon Press.10.21034/sr.148Search in Google Scholar

Geweke, J., and G. Amisano. 2011. “Hierarchical Markov Normal Mixture Models with Applications to Financial Asset Returns.” Journal of Applied Econometrics 26 (1): 1–29. https://doi.org/10.1002/jae.1119.Search in Google Scholar

Heinen, A. 2003. Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model. Also available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1117187.10.2139/ssrn.1117187Search in Google Scholar

Homburg, A., C. H. Weiss, L. C. Alwan, G. Frahm, and R. Göb. 2019. “Evaluating Approximate Point Forecasting of Count Processes.” Econometrics 7 (3). https://doi.org/10.3390/econometrics7030030.Search in Google Scholar

Homburg, A., C. H. Weiss, L. C. Alwan, G. Frahm, and R. Göb. 2020. “A Performance Analysis of Prediction Intervals for Count Time Series.” Journal of Forecasting 40 (4): 603–25. https://doi.org/10.1002/for.2729.Search in Google Scholar

McCabe, B. P. M., and G. M. Martin. 2005. “Bayesian Predictions of Low Count Time Series.” International Journal of Forecasting 21 (2): 315–30. https://doi.org/10.1016/j.ijforecast.2004.11.001.Search in Google Scholar

McCabe, B. P. M., G. M. Martin, and D. Harris. 2011. “Efficient Probabilistic Forecasts for Counts.” Journal of the Royal Statistical Society: Series B 73 (2): 253–72. https://doi.org/10.1111/j.1467-9868.2010.00762.x.Search in Google Scholar

Martino, L., H. Yang, D. Luengo, J. Kanniainen, and J. Corande. 2015. “A Fast Universal Self-Tuned Sampler within Gibbs Sampling.” Digital Signal Processing 47: 68–83. https://doi.org/10.1016/j.dsp.2015.04.005.Search in Google Scholar

Rydberg, T. H., and N. Shephard. 2000. BIN Models for Trade-by-Trade Data. Modelling the Number of Trades in a Fixed Interval of Time. Also available at https://ideas.repec.org/p/ecm/wc2000/0740.html.Search in Google Scholar

Weiss, C. H. 2018. An Introduction to Discrete-Valued Time Series. Hoboken: Wiley.10.1002/9781119097013Search in Google Scholar

Weiss, C. H., F. Zhu, and A. Hoshiyar. 2022. “Softplus INGARCH Models.” Statistica Sinica. (forthcoming).10.5705/ss.202020.0353Search in Google Scholar

Xu, H-Y., M. Xie, T. N. Goh, and X. Fu. 2012. “A Model for Integer-Valued Time Series with Conditional Overdispersion.” Computational Statistics & Data Analysis 56 (12): 4229–42. https://doi.org/10.1016/j.csda.2012.04.011.Search in Google Scholar

Zhu, F. 2011. “A Negative Binomial Integer-Valued GARCH Model.” Journal of Time Series Analysis 32 (1): 54–67. https://doi.org/10.1111/j.1467-9892.2010.00684.x.Search in Google Scholar

Zhu, F. 2012a. “Modeling Overdispersed or Underdispersed Count Data with Generalized Poisson Integer-Valued GARCH Models.” Journal of Mathematical Analysis and its Applications 389 (1): 58–71. https://doi.org/10.1016/j.jmaa.2011.11.042.Search in Google Scholar

Zhu, F. 2012b. “Zero-Inflated Poisson and Negative Binomial Integer-Valued GARCH Models.” Journal of Statistical Planning and Inference 142 (4): 826–39. https://doi.org/10.1016/j.jspi.2011.10.002.Search in Google Scholar

Zhu, F. 2012c. “Modeling Time Series of Counts with COM-Poisson INGARCH Models.” Mathematical and Computer Modelling 56 (9–10): 191–203. https://doi.org/10.1016/j.mcm.2011.11.069.Search in Google Scholar


Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/snde-2020-0095).


Received: 2020-08-13
Revised: 2021-08-30
Accepted: 2021-08-30
Published Online: 2021-09-13

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 2.5.2024 from https://www.degruyter.com/document/doi/10.1515/snde-2020-0095/html
Scroll to top button