IDEAS home Printed from https://ideas.repec.org/p/kud/kuiedp/1702.html

Cointegration between trends and their estimators in state space models and CVAR models

Author

Listed:
  • Søren Johansen

    (Department of Economics, University of Copenhagen)

  • Morten Nyboe Tabor

    (Department of Economics, University of Copenhagen)

Abstract

In a linear state space model Y(t)=BT(t)+e(t), we investigate if the unobserved trend, T(t), cointegrates with the predicted trend, E(t), and with the estimated predicted trend, in the sense that the spreads are stationary. We find that this result holds for the spread B(T(t)-E(t)) and the estimated spread. For the spread between the trend and the estimated trend, T(t)-E(t), however, cointegration depends on the identification of B. The same results are found, if the observations Y(t), from the state space model are analysed using a cointegrated vector autoregressive model, where the trend is defined as the common trend. Finally, we investigate cointegration between the spread beteween trends and their estimators based on the two models, and find the same results. We illustrate with two examples and confirm the results by a small simulation study.

Suggested Citation

  • Søren Johansen & Morten Nyboe Tabor, 2017. "Cointegration between trends and their estimators in state space models and CVAR models," Discussion Papers 17-02, University of Copenhagen. Department of Economics.
    • Handle: RePEc:kud:kuiedp:1702
    as

    Download full text from publisher

    File URL: http://www.econ.ku.dk/english/research/publications/wp/dp_2017/1702.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    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. 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.
    4. Kevin D. Hoover, 2021. "Erratum: Hoover, K.D. 2020. The Discovery of Long-Run Causal Order: A Preliminary Investigation. Econometrics 8: 31," Econometrics, MDPI, vol. 9(1), pages 1-1, February.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    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. 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.
    7. 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.
    8. Joaquín Bernal-Ramírez & Jair Ojeda-Joya & Camila Agudelo-Rivera & Felipe Clavijo-Ramírez & Carolina Durana-Ángel & Clark Granger-Castaño & Daniel Osorio-Rodríguez & Daniel Parra-Amado & José Pulido &, 2022. "Impacto macroeconómico del cambio climático en Colombia," Revista ESPE - Ensayos sobre Política Económica, Banco de la Republica de Colombia, issue 102, pages 1-62, July.
    9. Avanzi, Benjamin & Taylor, Greg & Vu, Phuong Anh & Wong, Bernard, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 50-71.
    10. Tomoya Mori & Daisuke Murakami, 2025. "Sustainability of cities under declining population and decreasing distance frictions: The case of Japan," KIER Working Papers 1117, Kyoto University, Institute of Economic Research.
    11. Wen Xu, 2016. "Estimation of Dynamic Panel Data Models with Stochastic Volatility Using Particle Filters," Econometrics, MDPI, vol. 4(4), pages 1-13, October.
    12. José Abraham López Machuca & Jorge Eduardo Mendoza Cota, 2017. "Salarios, desempleo y productividad laboral en la industria manufacturera mexicana. (Wage, Unemployment and Labor Productivity in the Mexican Manufacturing Industry)," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(2), pages 185-228, October.
    13. Blasques, F. & Francq, Christian & Laurent, Sébastien, 2024. "Autoregressive conditional betas," Journal of Econometrics, Elsevier, vol. 238(2).
    14. Alejandro Rodriguez & Esther Ruiz, 2009. "Bootstrap prediction intervals in state–space models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(2), pages 167-178, March.
    15. Parrini, Alessandro, 2013. "Importance Sampling for Portfolio Credit Risk in Factor Copula Models," MPRA Paper 103745, University Library of Munich, Germany.
    16. Salman Huseynov, 2021. "Long and short memory in dynamic term structure models," CREATES Research Papers 2021-15, Department of Economics and Business Economics, Aarhus University.
    17. Tsionas, Mike G., 2021. "Bayesian forecasting with the structural damped trend model," International Journal of Production Economics, Elsevier, vol. 234(C).
    18. Mustafa Naimoğlu & Serkan Şahin & Sefa Özbek, 2025. "Governance, Corruption, Trade Openness, and Innovation: Key Drivers of Green Growth and Sustainable Development in Türkiye," Sustainable Development, John Wiley & Sons, Ltd., vol. 33(3), pages 4147-4162, June.
    19. Ansgar Belke & Robert Czudaj, 2010. "Is Euro Area Money Demand (Still) Stable? Cointegrated VAR Versus Single Equation Techniques," Applied Economics Quarterly (formerly: Konjunkturpolitik), Duncker & Humblot, Berlin, vol. 56(4), pages 285-315.
    20. 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.

    More about this item

    Keywords

    ;
    ;
    ;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

    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:kud:kuiedp:1702. 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: Thomas Hoffmann (email available below). General contact details of provider: https://edirc.repec.org/data/okokudk.html .

    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.