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On the invertibility of time series models

Author

Listed:
  • Granger, C. W. J.
  • Andersen, Allan

Abstract

A generalized definition of invertibility is proposed and applied to linear, non-linear and bilinear models. It is shown that some recently studied non-linear models are not invertible, but conditions for invertibility can be achieved for the other models.

Suggested Citation

  • Granger, C. W. J. & Andersen, Allan, 1978. "On the invertibility of time series models," Stochastic Processes and their Applications, Elsevier, vol. 8(1), pages 87-92, November.
    • Handle: RePEc:eee:spapps:v:8:y:1978:i:1:p:87-92
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    Citations

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    Cited by:

    1. Koop, Gary & Ley, Eduardo & Osiewalski, Jacek & Steel, Mark F. J., 1997. "Bayesian analysis of long memory and persistence using ARFIMA models," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 149-169.
    2. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    3. F Blasques & P Gorgi & S Koopman & O Wintenberger, 2016. "Feasible Invertibility Conditions for Maximum Likelihood Estimation for Observation-Driven Models," Papers 1610.02863, arXiv.org.
    4. Olivier Wintenberger, 2013. "Continuous Invertibility and Stable QML Estimation of the EGARCH(1,1) Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 846-867, December.
    5. Zaffaroni, Paolo & d'Italia, Banca, 2003. "Gaussian inference on certain long-range dependent volatility models," Journal of Econometrics, Elsevier, vol. 115(2), pages 199-258, August.
    6. Ghouse, Ghulam & Khan, Saud Ahmed & Arshad, Muhammad, 2015. "Time Varying Volatility Modeling of Pakistani and leading foreign stock markets," MPRA Paper 70080, University Library of Munich, Germany.
    7. Martinez Oscar & Olmo Jose, 2012. "A Nonlinear Threshold Model for the Dependence of Extremes of Stationary Sequences," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(3), pages 1-39, September.
    8. Hai‐Bin Wang, 2008. "Nonlinear ARMA models with functional MA coefficients," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 1032-1056, November.
    9. Shiqing Ling & Liang Peng & Fukang Zhu, 2015. "Inference For A Special Bilinear Time-Series Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(1), pages 61-66, January.
    10. Martínez, Oscar, 2003. "Threshold integrated moving average models: does size matter? maybe so," DE - Documentos de Trabajo. Economía. DE 16008, Universidad Carlos III de Madrid. Departamento de Economía.
    11. Christian M. Hafner & Dimitra Kyriakopoulou, 2021. "Exponential-Type GARCH Models With Linear-in-Variance Risk Premium," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 589-603, March.
    12. Robert F. Engle & Aaron D. Smith, 1999. "Stochastic Permanent Breaks," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 553-574, November.
    13. Blasques, Francisco & van Brummelen, Janneke & Koopman, Siem Jan & Lucas, André, 2022. "Maximum likelihood estimation for score-driven models," Journal of Econometrics, Elsevier, vol. 227(2), pages 325-346.
    14. Francisco Blasques & Paolo Gorgi & Siem Jan Koopman & Olivier Wintenberger, 2016. "Feasible Invertibility Conditions and Maximum Likelihood Estimation for Observation-Driven Models," Tinbergen Institute Discussion Papers 16-082/III, Tinbergen Institute.
    15. Zaffaroni, Paolo, 2009. "Whittle estimation of EGARCH and other exponential volatility models," Journal of Econometrics, Elsevier, vol. 151(2), pages 190-200, August.
    16. Man Wang & Kun Chen & Qin Luo & Chao Cheng, 2018. "Multi-Step Inflation Prediction with Functional Coefficient Autoregressive Model," Sustainability, MDPI, vol. 10(6), pages 1-16, May.
    17. F Blasques & P Gorgi & S J Koopman & O Wintenberger, 2016. "Feasible Invertibility Conditions for Maximum Likelihood Estimation for Observation-Driven Models ," Working Papers hal-01377971, HAL.
    18. González Gómez, Andrés, 2004. "A smooth permanent surge process," SSE/EFI Working Paper Series in Economics and Finance 572, Stockholm School of Economics.

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