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Artificial neural networks and time series of counts: A class of nonlinear INGARCH models

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  • Malte Jahn

Abstract

Time series of counts are frequently analyzed using generalized integer-valued autoregressive models with conditional heteroskedasticity (INGARCH). These models employ response functions to map a vector of past observations and past conditional expectations to the conditional expectation of the present observation. In this paper, it is shown how INGARCH models can be combined with artificial neural network (ANN) response functions to obtain a class of nonlinear INGARCH models. The ANN framework allows for the interpretation of many existing INGARCH models as a degenerate version of a corresponding neural model. Details on maximum likelihood estimation, marginal effects and confidence intervals are given. The empirical analysis of time series of bounded and unbounded counts reveals that the neural INGARCH models are able to outperform reasonable degenerate competitor models in terms of the information loss.

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  • Malte Jahn, 2023. "Artificial neural networks and time series of counts: A class of nonlinear INGARCH models," Papers 2304.01025, arXiv.org.
    • Handle: RePEc:arx:papers:2304.01025
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    1. Fokianos, Konstantinos & Rahbek, Anders & Tjøstheim, Dag, 2009. "Poisson Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1430-1439.
    2. Carmen M. Reinhart & Kenneth S. Rogoff, 2014. "This Time is Different: A Panoramic View of Eight Centuries of Financial Crises," Annals of Economics and Finance, Society for AEF, vol. 15(2), pages 215-268, November.
    3. Carmen M. Reinhart & Kenneth S. Rogoff, 2009. "Varieties of Crises and Their Dates," Introductory Chapters, in: This Time Is Different: Eight Centuries of Financial Folly, Princeton University Press.
    4. Jahn, Malte, 2020. "Artificial neural network regression models in a panel setting: Predicting economic growth," Economic Modelling, Elsevier, vol. 91(C), pages 148-154.
    5. Fokianos, Konstantinos & Tjøstheim, Dag, 2011. "Log-linear Poisson autoregression," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 563-578, March.
    6. Kock, Anders Bredahl & Teräsvirta, Timo, 2014. "Forecasting performances of three automated modelling techniques during the economic crisis 2007–2009," International Journal of Forecasting, Elsevier, vol. 30(3), pages 616-631.
    7. Sirchenko Andrei, 2020. "A model for ordinal responses with heterogeneous status quo outcomes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 24(1), pages 1-16, February.
    8. Tkacz, Greg, 2001. "Neural network forecasting of Canadian GDP growth," International Journal of Forecasting, Elsevier, vol. 17(1), pages 57-69.
    9. Sirchenko Andrei, 2012. "A model for ordinal responses with an application to policy interest rate," EERC Working Paper Series 12/13e, EERC Research Network, Russia and CIS.
    10. Tobias A. Möller & Christian H. Weiß & Hee-Young Kim & Andrei Sirchenko, 2018. "Modeling Zero Inflation in Count Data Time Series with Bounded Support," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 589-609, June.
    11. René Ferland & Alain Latour & Driss Oraichi, 2006. "Integer‐Valued GARCH Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 923-942, November.
    12. Dungey Mardi & Martin Vance L. & Tang Chrismin & Tremayne Andrew, 2020. "A threshold mixed count time series model: estimation and application," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 24(2), pages 1-18, April.
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