IDEAS home Printed from https://ideas.repec.org/a/taf/emetrv/v28y2009i1-3p121-145.html
   My bibliography  Save this article

Representation of Cointegrated Autoregressive Processes with Application to Fractional Processes

Author

Listed:
  • Søren Johansen

Abstract

We analyze vector autoregressive processes using the matrix valued characteristic polynomial. The purpose of this article is to give a survey of the mathematical results on inversion of a matrix polynomial in case there are unstable roots, to study integrated and cointegrated processes. The new results are in the I(2) representation, which contains explicit formulas for the first two terms and a useful property of the third. We define a new error correction model for fractional processes and derive a representation of the solution.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:emetrv:v:28:y:2009:i:1-3:p:121-145
    DOI: 10.1080/07474930802387977
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/07474930802387977
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/07474930802387977?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. Mario Faliva & Maria Grazia Zoia, 2006. "Topics in Dynamic Model Analysis," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-29239-5, October.
    2. Dietmar Bauer & Martin Wagner, 2002. "A Canonical Form for Unit Root Processes in the State Space Framework," Diskussionsschriften dp0204, Universitaet Bern, Departement Volkswirtschaft.
    3. Engle, R. F. & Granger, C. W. J. (ed.), 1991. "Long-Run Economic Relationships: Readings in Cointegration," OUP Catalogue, Oxford University Press, number 9780198283393.
    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. Beare, Brendan K. & Seo, Won-Ki, 2020. "Representation Of I(1) And I(2) Autoregressive Hilbertian Processes," Econometric Theory, Cambridge University Press, vol. 36(5), pages 773-802, October.
    2. Massimo Franchi & Paolo Paruolo, 2015. "Minimality of State Space Solutions of DSGE Models and Existence Conditions for Their VAR Representation," Computational Economics, Springer;Society for Computational Economics, vol. 46(4), pages 613-626, December.
    3. 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.
    4. Franchi, Massimo & Paruolo, Paolo, 2011. "A characterization of vector autoregressive processes with common cyclical features," Journal of Econometrics, Elsevier, vol. 163(1), pages 105-117, July.
    5. Daniela Osterrieder & Daniel Ventosa-Santaulària & J. Eduardo Vera-Valdés, 2015. "Unbalanced Regressions and the Predictive Equation," CREATES Research Papers 2015-09, Department of Economics and Business Economics, Aarhus University.
    6. Federico Carlini & Katarzyna Lasak, 2014. "On an Estimation Method for an Alternative Fractionally Cointegrated Model," CREATES Research Papers 2014-15, Department of Economics and Business Economics, Aarhus University.
    7. 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.
    8. Massimo Franchi & Paolo Paruolo, 2012. "On ABCs (and Ds) of VAR representations of DSGE models," Working Paper series 56_12, Rimini Centre for Economic Analysis, revised Aug 2012.
    9. Katarzyna Łasak & Carlos Velasco, 2015. "Fractional Cointegration Rank Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 241-254, April.
    10. de Truchis, Gilles, 2013. "Approximate Whittle analysis of fractional cointegration and the stock market synchronization issue," Economic Modelling, Elsevier, vol. 34(C), pages 98-105.
    11. Massimo Franchi & Paolo Paruolo, 2019. "A general inversion theorem for cointegration," Econometric Reviews, Taylor & Francis Journals, vol. 38(10), pages 1176-1201, November.
    12. Chen, Cathy Yi-Hsuan & Chiang, Thomas C. & Härdle, Wolfgang Karl, 2016. "Downside risk and stock returns: An empirical analysis of the long-run and short-run dynamics from the G-7 Countries," SFB 649 Discussion Papers 2016-001, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    13. Berta, P. & Lovaglio, P.G. & Paruolo, P. & Verzillo, S., 2020. "Real Time Forecasting of Covid-19 Intensive Care Units demand," Health, Econometrics and Data Group (HEDG) Working Papers 20/16, HEDG, c/o Department of Economics, University of York.
    14. 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.
    15. Katarzyna Łasak & Johannes Lont, 2020. "Observation Driven Long Run Equilibria," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 551-575, February.
    16. Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 67-77, September.
    17. Brendan K. Beare & Juwon Seo & Won-Ki Seo, 2017. "Cointegrated Linear Processes in Hilbert Space," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 1010-1027, November.
    18. Chen, Xiaoyu & Chiang, Thomas C., 2016. "Stock returns and economic forces—An empirical investigation of Chinese markets," Global Finance Journal, Elsevier, vol. 30(C), pages 45-65.
    19. Federico Carlini & Katarzyna (K.A.) Lasak, 2018. "Likelihood based inference for an Identifiable Fractional Vector Error Correction Model," Tinbergen Institute Discussion Papers 18-085/III, Tinbergen Institute.
    20. Tim Bollerslev & Daniela Osterrieder & Natalia Sizova & George Tauchen, 2011. "Risk and Return: Long-Run Relationships, Fractional Cointegration, and Return Predictability," CREATES Research Papers 2011-51, Department of Economics and Business Economics, Aarhus University.
    21. repec:hum:wpaper:sfb649dp2016-001 is not listed on IDEAS
    22. H. Peter Boswijk & Paolo Paruolo, 2017. "Likelihood Ratio Tests of Restrictions on Common Trends Loading Matrices in I(2) VAR Systems," Econometrics, MDPI, vol. 5(3), pages 1-17, June.

    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. Muellbauer, John & Sinclair, Peter & Aron, Janine & Farrell, Greg, 2010. "Exchange Rate Pass-through and Monetary Policy in South Africa," CEPR Discussion Papers 8153, C.E.P.R. Discussion Papers.
    2. Yap, Wei Yim & Lam, Jasmine S.L., 2006. "Competition dynamics between container ports in East Asia," Transportation Research Part A: Policy and Practice, Elsevier, vol. 40(1), pages 35-51, January.
    3. Daniel Levy, 1995. "Investment-saving comovement under endogenous fiscal policy," Open Economies Review, Springer, vol. 6(3), pages 237-254, July.
    4. Erie Febrian & Aldrin Herwany, 2009. "Volatility Forecasting Models and Market Co-Integration: A Study on South-East Asian Markets," Working Papers in Economics and Development Studies (WoPEDS) 200911, Department of Economics, Padjadjaran University, revised Sep 2009.
    5. Janine Aron & John Muellbauer, 2006. "Housing Wealth, Credit Conditions and Consumption," CSAE Working Paper Series 2006-08, Centre for the Study of African Economies, University of Oxford.
    6. Marcus Box & Karl Gratzer & Xiang Lin, 2020. "Destructive entrepreneurship in the small business sector: bankruptcy fraud in Sweden, 1830–2010," Small Business Economics, Springer, vol. 54(2), pages 437-457, February.
    7. Moosa, Imad A. & Choe, Chongwoo, 1998. "Is the Korean economy export-driven?," Economic Modelling, Elsevier, vol. 15(2), pages 237-255, April.
    8. Cashin, Paul & Mohaddes, Kamiar & Raissi, Maziar & Raissi, Mehdi, 2014. "The differential effects of oil demand and supply shocks on the global economy," Energy Economics, Elsevier, vol. 44(C), pages 113-134.
    9. Dierk HERZER & Felicitas NOWAK‐LEHMANN D. & Boriss SILIVERSTOVS, 2006. "Export‐Led Growth In Chile: Assessing The Role Of Export Composition In Productivity Growth," The Developing Economies, Institute of Developing Economies, vol. 44(3), pages 306-328, September.
    10. Acaravici, Ali, 2010. "Structural Breaks, Electricity Consumption and Economic Growth: Evidence from Turkey," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 140-154, July.
    11. Zapata, Hector O. & Gil, Jose M., 1999. "Cointegration and causality in international agricultural economics research," Agricultural Economics, Blackwell, vol. 20(1), pages 1-9, January.
    12. Husted, Steven & MacDonald, Ronald, 1998. "Monetary-based models of the exchange rate: a panel perspective," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 8(1), pages 1-19, January.
    13. Jan Overgaard Olesen, "undated". "A Simple Explanation of Stock Price Behavior in the Long Run: Evidence for Denmark," EPRU Working Paper Series 00-09, Economic Policy Research Unit (EPRU), University of Copenhagen. Department of Economics.
    14. Bruno Breyer Caldas & João Frois Caldeira & Guilherme Vale Moura, 2016. "Is Pairs Trading Performance Sensitive To The Methodologies?: A Comparison," Anais do XLII Encontro Nacional de Economia [Proceedings of the 42nd Brazilian Economics Meeting] 130, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    15. Goh, Soo Khoon & Mithani, Dawood, 2000. "Deviation from Purchasing Power Parity: Evidence from Malaysia, 1973–1997," MPRA Paper 51922, University Library of Munich, Germany.
    16. Beenstock, Michael & Reingewertz, Yaniv & Paldor, Nathan, 2016. "Testing the historic tracking of climate models," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1234-1246.
    17. Ellington, Michael & Milas, Costas, 2019. "Global liquidity, money growth and UK inflation," Journal of Financial Stability, Elsevier, vol. 42(C), pages 67-74.
    18. Abdul Qayyum, 2000. "Demand for Real Money Balances by the Business Sector: An Econometric Investigation," The Pakistan Development Review, Pakistan Institute of Development Economics, vol. 39(4), pages 857-873.
    19. Campos, Julia & Ericsson, Neil R. & Hendry, David F., 1996. "Cointegration tests in the presence of structural breaks," Journal of Econometrics, Elsevier, vol. 70(1), pages 187-220, January.
    20. Dauda, Risikat Oladoyin S., 2011. "Effect of Public Educational Spending and Macroeconomic Uncertainty on Schooling Outcomes: Evidence from Nigeria," Journal of Economics, Finance and Administrative Science, Universidad ESAN, vol. 16(31), pages 7-21.

    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:taf:emetrv:v:28:y:2009:i:1-3:p:121-145. 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: the person in charge (email available below). General contact details of provider: http://www.tandfonline.com/LECR20 .

    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.