IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2005.03988.html
   My bibliography  Save this paper

Fractional trends in unobserved components models

Author

Listed:
  • Tobias Hartl
  • Rolf Tschernig
  • Enzo Weber

Abstract

We develop a generalization of unobserved components models that allows for a wide range of long-run dynamics by modelling the permanent component as a fractionally integrated process. The model does not require stationarity and can be cast in state space form. In a multivariate setup, fractional trends may yield a cointegrated system. We derive the Kalman filter estimator for the common fractionally integrated component and establish consistency and asymptotic (mixed) normality of the maximum likelihood estimator. We apply the model to extract a common long-run component of three US inflation measures, where we show that the $I(1)$ assumption is likely to be violated for the common trend.

Suggested Citation

  • Tobias Hartl & Rolf Tschernig & Enzo Weber, 2020. "Fractional trends in unobserved components models," Papers 2005.03988, arXiv.org, revised May 2020.
    • Handle: RePEc:arx:papers:2005.03988
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2005.03988
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Søren Johansen & Morten Ørregaard Nielsen, 2012. "Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model," Econometrica, Econometric Society, vol. 80(6), pages 2667-2732, November.
    2. Morten Ørregaard Nielsen, 2015. "Asymptotics for the Conditional-Sum-of-Squares Estimator in Multivariate Fractional Time-Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 154-188, March.
    3. Rolf Tschernig & Enzo Weber & Roland Weigand, 2013. "Long-Run Identification in a Fractionally Integrated System," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 438-450, October.
    4. James C. Morley & Charles R. Nelson & Eric Zivot, 2003. "Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 235-243, May.
    5. Hassler, Uwe & Wolters, Jurgen, 1995. "Long Memory in Inflation Rates: International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 37-45, January.
    6. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    7. Johansen, Søren & Nielsen, Morten Ørregaard, 2010. "Likelihood inference for a nonstationary fractional autoregressive model," Journal of Econometrics, Elsevier, vol. 158(1), pages 51-66, September.
    8. James H. Stock & Mark W. Watson, 2016. "Core Inflation and Trend Inflation," The Review of Economics and Statistics, MIT Press, vol. 98(4), pages 770-784, October.
    9. Tommaso Proietti, 2016. "Component-wise Representations of Long-memory Models and Volatility Prediction," Journal of Financial Econometrics, Oxford University Press, vol. 14(4), pages 668-692.
    10. Peter M Robinson, 2006. "Conditional-Sum-of-Squares Estimation ofModels for Stationary Time Series with Long Memory," STICERD - Econometrics Paper Series 505, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    11. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    12. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    13. Johansen, SØren, 2008. "A Representation Theory For A Class Of Vector Autoregressive Models For Fractional Processes," Econometric Theory, Cambridge University Press, vol. 24(3), pages 651-676, June.
    14. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737, January.
    15. Granger, C. W. J. & Newbold, Paul, 1986. "Forecasting Economic Time Series," Elsevier Monographs, Elsevier, edition 2, number 9780122951831 edited by Shell, Karl.
    16. Robinson, Peter, 2006. "Conditional-sum-of-squares estimation of models for stationary time series with long memory," LSE Research Online Documents on Economics 4536, London School of Economics and Political Science, LSE Library.
    17. Ulrich K. Müller & Mark W. Watson, 2018. "Long†Run Covariability," Econometrica, Econometric Society, vol. 86(3), pages 775-804, May.
    18. Tobias Hartl & Roland Jucknewitz, 2022. "Approximate state space modelling of unobserved fractional components," Econometric Reviews, Taylor & Francis Journals, vol. 41(1), pages 75-98, January.
    19. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    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. Tobias Hartl & Rolf Tschernig & Enzo Weber, 2020. "Fractional trends and cycles in macroeconomic time series," Papers 2005.05266, arXiv.org, revised May 2020.
    2. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    3. Hartl, Tobias, 2021. "Monitoring the pandemic: A fractional filter for the COVID-19 contact rate," VfS Annual Conference 2021 (Virtual Conference): Climate Economics 242380, Verein für Socialpolitik / German Economic Association.
    4. Tobias Hartl, 2021. "Monitoring the pandemic: A fractional filter for the COVID-19 contact rate," Papers 2102.10067, arXiv.org.
    5. Søren Johansen & Morten Ørregaard Nielsen, 2012. "The role of initial values in nonstationary fractional time series models," Discussion Papers 12-18, University of Copenhagen. Department of Economics.
    6. Tobias Hartl & Roland Weigand, 2018. "Multivariate Fractional Components Analysis," Papers 1812.09149, arXiv.org, revised Jan 2019.
    7. Tobias Hartl, 2020. "Macroeconomic Forecasting with Fractional Factor Models," Papers 2005.04897, arXiv.org.
    8. Johansen, Søren & Nielsen, Morten Ørregaard, 2016. "The Role Of Initial Values In Conditional Sum-Of-Squares Estimation Of Nonstationary Fractional Time Series Models," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1095-1139, October.
    9. Luis A. Gil-Alana & Antonio Moreno & Seonghoon Cho, 2012. "The Deaton paradox in a long memory context with structural breaks," Applied Economics, Taylor & Francis Journals, vol. 44(25), pages 3309-3322, September.
    10. Yuliya Lovcha & Alejandro Perez-Laborda, 2017. "Structural shocks and dynamic elasticities in a long memory model of the US gasoline retail market," Empirical Economics, Springer, vol. 53(2), pages 405-422, September.
    11. Samet Gunay, 2018. "Fractionally Cointegrated Vector Autoregression Model: Evaluation of High/Low and Close/Open Spreads for Precious Metals," SAGE Open, , vol. 8(4), pages 21582440188, November.
    12. Carlos D. Ramirez, 2024. "The effect of economic policy uncertainty under fractional integration," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 23(1), pages 89-110, January.
    13. Alia Afzal & Philipp Sibbertsen, 2021. "Modeling fractional cointegration between high and low stock prices in Asian countries," Empirical Economics, Springer, vol. 60(2), pages 661-682, February.
    14. Aye, Goodness C. & Carcel, Hector & Gil-Alana, Luis A. & Gupta, Rangan, 2017. "Does gold act as a hedge against inflation in the UK? Evidence from a fractional cointegration approach over 1257 to 2016," Resources Policy, Elsevier, vol. 54(C), pages 53-57.
    15. Federico Carlini & Paolo Santucci de Magistris, 2019. "Resuscitating the co-fractional model of Granger (1986)," Discussion Papers 19/01, University of Nottingham, Granger Centre for Time Series Econometrics.
    16. Luis Uzeda, 2022. "State Correlation and Forecasting: A Bayesian Approach Using Unobserved Components Models," Advances in Econometrics, in: Essays in Honour of Fabio Canova, volume 44, pages 25-53, Emerald Group Publishing Limited.
    17. Uwe Hassler & Marc-Oliver Pohle, 2019. "Forecasting under Long Memory and Nonstationarity," Papers 1910.08202, arXiv.org.
    18. Morten Ørregaard Nielsen & Sergei S. Shibaev, 2015. "Forecasting daily political opinion polls using the fractionally cointegrated VAR model," Working Paper 1340, Economics Department, Queen's University.
    19. Lovcha, Yuliya & Perez-Laborda, Alejandro, 2018. "Monetary policy shocks, inflation persistence, and long memory," Journal of Macroeconomics, Elsevier, vol. 55(C), pages 117-127.
    20. Maggie E. C. Jones & Morten Ørregaard Nielsen & Michał Ksawery Popiel, 2014. "A fractionally cointegrated VAR analysis of economic voting and political support," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 47(4), pages 1078-1130, November.

    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:2005.03988. 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.