IDEAS home Printed from https://ideas.repec.org/a/gam/jecnmx/v5y2017i3p36-d109242.html
   My bibliography  Save this article

Cointegration between Trends and Their Estimators in State Space Models and Cointegrated Vector Autoregressive Models

Author

Listed:
  • Søren Johansen

    (Department of Economics, University of Copenhagen, Øster Farimagsgade 5, Building 26, 1353 Copenhagen K, Denmark)

  • Morten Nyboe Tabor

    (Department of Economics, University of Copenhagen, Øster Farimagsgade 5, Building 26, 1353 Copenhagen K, Denmark)

Abstract

A state space model with an unobserved multivariate random walk and a linear observation equation is studied. The purpose is to find out when the extracted trend cointegrates with its estimator, in the sense that a linear combination is asymptotically stationary. It is found that this result holds for the linear combination of the trend that appears in the observation equation. If identifying restrictions are imposed on either the trend or its coefficients in the linear observation equation, it is shown that there is cointegration between the identified trend and its estimator, if and only if the estimators of the coefficients in the observation equations are consistent at a faster rate than the square root of sample size. The same results are found if the observations from the state space model are analysed using a cointegrated vector autoregressive model. The findings are illustrated by a small simulation study.

Suggested Citation

  • Søren Johansen & Morten Nyboe Tabor, 2017. "Cointegration between Trends and Their Estimators in State Space Models and Cointegrated Vector Autoregressive Models," Econometrics, MDPI, vol. 5(3), pages 1-15, August.
    • Handle: RePEc:gam:jecnmx:v:5:y:2017:i:3:p:36-:d:109242
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2225-1146/5/3/36/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2225-1146/5/3/36/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Johansen, Søren, 2010. "Some identification problems in the cointegrated vector autoregressive model," Journal of Econometrics, Elsevier, vol. 158(2), pages 262-273, October.
    2. Harvey, Andrew, 2006. "Forecasting with Unobserved Components Time Series Models," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 7, pages 327-412, Elsevier.
    3. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    4. Saikkonen, Pentti, 1992. "Estimation and Testing of Cointegrated Systems by an Autoregressive Approximation," Econometric Theory, Cambridge University Press, vol. 8(1), pages 1-27, March.
    5. Saikkonen, Pentti & Lütkepohl, HELMUT, 1996. "Infinite-Order Cointegrated Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(5), pages 814-844, December.
    6. Johansen, Søren & Juselius, Katarina, 2014. "An asymptotic invariance property of the common trends under linear transformations of the data," Journal of Econometrics, Elsevier, vol. 178(P2), pages 310-315.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sergej Gričar & Štefan Bojnec, 2021. "Technical Analysis of Tourism Price Process in the Eurozone," JRFM, MDPI, vol. 14(11), pages 1-25, October.
    2. Poncela, Pilar & Ruiz, Esther & Miranda, Karen, 2021. "Factor extraction using Kalman filter and smoothing: This is not just another survey," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1399-1425.
    3. Kevin D. Hoover, 2020. "The Discovery of Long-Run Causal Order: A Preliminary Investigation," Econometrics, MDPI, vol. 8(3), pages 1-25, August.
    4. Franchi, Massimo, 2018. "Testing for cointegration in I(1) state space systems via a finite order approximation," Economics Letters, Elsevier, vol. 165(C), pages 73-76.

    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. Søren Johansen, 2019. "Cointegration and Adjustment in the CVAR(∞) Representation of Some Partially Observed CVAR(1) Models," Econometrics, MDPI, vol. 7(1), pages 1-10, January.
    2. Guillermo Carlomagno & Antoni Espasa, 2021. "Discovering Specific Common Trends in a Large Set of Disaggregates: Statistical Procedures, their Properties and an Empirical Application," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(3), pages 641-662, June.
    3. Soeren Johansen, 2018. "Cointegration and adjustment in the infinite order CVAR representation of some partially observed CVAR(1) models," Discussion Papers 18-05, University of Copenhagen. Department of Economics.
    4. Søren Johansen & Morten Nyboe Tabor, 2017. "Cointegration between trends and their estimators in state space models and CVAR models," CREATES Research Papers 2017-11, Department of Economics and Business Economics, Aarhus University.
    5. Franchi, Massimo, 2018. "Testing for cointegration in I(1) state space systems via a finite order approximation," Economics Letters, Elsevier, vol. 165(C), pages 73-76.
    6. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107034723.
    7. David E. Allen & Chialin Chang & Michael McAleer & Abhay K Singh, 2018. "A cointegration analysis of agricultural, energy and bio-fuel spot, and futures prices," Applied Economics, Taylor & Francis Journals, vol. 50(7), pages 804-823, February.
    8. 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.
    9. Saikkonen, Pentti & Luukkonen, Ritva, 1997. "Testing cointegration in infinite order vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 93-126, November.
    10. Cristea, R. G., 2020. "Can Alternative Data Improve the Accuracy of Dynamic Factor Model Nowcasts?," Cambridge Working Papers in Economics 20108, Faculty of Economics, University of Cambridge.
    11. El-Shagi, Makram & Giesen, Sebastian, 2013. "Money and inflation: Consequences of the recent monetary policy," Journal of Policy Modeling, Elsevier, vol. 35(4), pages 520-537.
    12. Buncic, Daniel, 2020. "Econometric issues with Laubach and Williams’ estimates of the natural rate of interest," Working Paper Series 397, Sveriges Riksbank (Central Bank of Sweden).
    13. Bauer, Dietmar & Wagner, Martin, 2002. "Estimating cointegrated systems using subspace algorithms," Journal of Econometrics, Elsevier, vol. 111(1), pages 47-84, November.
    14. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521520911.
    15. Lutkepohl, Helmut & Saikkonen, Pentti, 1997. "Impulse response analysis in infinite order cointegrated vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 127-157, November.
    16. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    17. Qu, Zhongjun & Perron, Pierre, 2007. "A Modified Information Criterion For Cointegration Tests Based On A Var Approximation," Econometric Theory, Cambridge University Press, vol. 23(4), pages 638-685, August.
    18. Martin Wagner, 2010. "Cointegration analysis with state space models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(3), pages 273-305, September.
    19. DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics 0649, Faculty of Economics, University of Cambridge.
    20. El-Shagi, Makram & Giesen, Sebastian, 2010. "Money and Inflation: The Role of Persistent Velocity Movements," IWH Discussion Papers 2/2010, Halle Institute for Economic Research (IWH).

    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:gam:jecnmx:v:5:y:2017:i:3:p:36-:d:109242. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.