IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v178y2014ip2p310-315.html
   My bibliography  Save this article

An asymptotic invariance property of the common trends under linear transformations of the data

Author

Listed:
  • Johansen, Søren
  • Juselius, Katarina

Abstract

It is well known that if Xt is a nonstationary process and Yt is a linear function of Xt, then cointegration of Yt implies cointegration of Xt. We want to find an analogous result for common trends if Xt is generated by a finite order VAR with i.i.d. (0,Ωx) errors εxt. We first show that Yt has an infinite order VAR representation in terms of its white noise prediction errors, εyt, which are a linear process in εxt, the prediction error for Xt. We then apply this result to show that the limit of the common trends for Yt generated by εyt, are linear functions of the common trends for Xt, generated by εxt.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:178:y:2014:i:p2:p:310-315
    DOI: 10.1016/j.jeconom.2013.08.029
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407613001930
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2013.08.029?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Giese, Julia V., 2008. "Level, Slope, Curvature: Characterising the Yield Curve in a Cointegrated VAR Model," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 2, pages 1-20.
    2. 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.
    3. Søren Johansen, 2009. "Representation of Cointegrated Autoregressive Processes with Application to Fractional Processes," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 121-145.
    4. Saikkonen, Pentti & Lütkepohl, HELMUT, 1996. "Infinite-Order Cointegrated Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(5), pages 814-844, December.
    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. Katarina Juselius, 2021. "Searching for a Theory That Fits the Data: A Personal Research Odyssey," Econometrics, MDPI, vol. 9(1), pages 1-27, February.
    2. 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.
    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. Anders Rygh Swensen, 2022. "On causal and non‐causal cointegrated vector autoregressive time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 178-196, March.
    7. 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.
    8. 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.

    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. 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.
    2. Saikkonen, Pentti & Luukkonen, Ritva, 1997. "Testing cointegration in infinite order vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 93-126, November.
    3. Søren Johansen & Katarina Juselius, 2010. "An Invariance Property of the Common Trends under Linear Transformations of the Data," Discussion Papers 10-30, University of Copenhagen. Department of Economics.
    4. Bauer, Dietmar & Wagner, Martin, 2002. "Estimating cointegrated systems using subspace algorithms," Journal of Econometrics, Elsevier, vol. 111(1), pages 47-84, November.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Yuanyuan Li & Dietmar Bauer, 2020. "Modeling I(2) Processes Using Vector Autoregressions Where the Lag Length Increases with the Sample Size," Econometrics, MDPI, vol. 8(3), pages 1-28, September.
    11. 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.
    12. Georgios Bertsatos & Plutarchos Sakellaris & Mike G. Tsionas, 2022. "Extensions of the Pesaran, Shin and Smith (2001) bounds testing procedure," Empirical Economics, Springer, vol. 62(2), pages 605-634, February.
    13. Athanasopoulos, George & de Carvalho Guillén, Osmani Teixeira & Issler, João Victor & Vahid, Farshid, 2011. "Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions," Journal of Econometrics, Elsevier, vol. 164(1), pages 116-129, September.
    14. Candelon, Bertrand & Lieb, Lenard, 2013. "Fiscal policy in good and bad times," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2679-2694.
    15. 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.
    16. Mohammad I. Elian & Khalid M. Kisswani, 2018. "Oil price changes and stock market returns: cointegration evidence from emerging market," Economic Change and Restructuring, Springer, vol. 51(4), pages 317-337, November.
    17. Mauricio, Jose Alberto, 2006. "Exact maximum likelihood estimation of partially nonstationary vector ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3644-3662, August.
    18. 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.
    19. Olimpia Neagu, 2019. "The Link between Economic Complexity and Carbon Emissions in the European Union Countries: A Model Based on the Environmental Kuznets Curve (EKC) Approach," Sustainability, MDPI, vol. 11(17), pages 1-27, August.
    20. Richard H. Clarida & Lucio Sarno & Mark P. Taylor & Giorgio Valente, 2006. "The Role of Asymmetries and Regime Shifts in the Term Structure of Interest Rates," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1193-1224, May.

    More about this item

    Keywords

    Cointegration vectors; Common trends; Prediction errors;
    All these 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

    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:eee:econom:v:178:y:2014:i:p2:p:310-315. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.