IDEAS home Printed from https://ideas.repec.org/p/aah/create/2013-44.html
   My bibliography  Save this paper

On the identification of fractionally cointegrated VAR models with the F(d) condition

Author

Listed:
  • Federico Carlini

    (Aarhus University and CREATES)

  • Paolo Santucci de Magistris

    (Aarhus University and CREATES)

Abstract

This paper discusses identification problems in the fractionally cointegrated system of Johansen (2008) and Johansen and Nielsen (2012). The identification problem arises when the lag structure is over-specified, such that there exist several equivalent reparametrization of the model associated with different fractional integration and cointegration parameters. The properties of these multiple non-identified sub-models are studied and a necessary and sufficient condition for the identification of the fractional parameters of the system is provided. The condition is named F(d). The assessment of the F(d) condition in the empirical analysis is relevant for the determination of the fractional parameters as well as the lag structure.

Suggested Citation

  • Federico Carlini & Paolo Santucci de Magistris, 2013. "On the identification of fractionally cointegrated VAR models with the F(d) condition," CREATES Research Papers 2013-44, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2013-44
    as

    Download full text from publisher

    File URL: https://repec.econ.au.dk/repec/creates/rp/13/rp13_44.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. Avarucci, Marco & Velasco, Carlos, 2009. "A Wald test for the cointegration rank in nonstationary fractional systems," Journal of Econometrics, Elsevier, vol. 151(2), pages 178-189, August.
    3. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    4. Franchi, Massimo, 2010. "A Representation Theory For Polynomial Cofractionality In Vector Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 26(4), pages 1201-1217, August.
    5. Breitung, Jorg & Hassler, Uwe, 2002. "Inference on the cointegration rank in fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 110(2), pages 167-185, October.
    6. Katarzyna Łasak & Carlos Velasco, 2015. "Fractional Cointegration Rank Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 241-254, April.
    7. Tschernig, Rolf & Weber, Enzo & Weigand, Roland, 2013. "Fractionally Integrated VAR Models with a Fractional Lag Operator and Deterministic Trends: Finite Sample Identification and Two-step Estimation," University of Regensburg Working Papers in Business, Economics and Management Information Systems 471, University of Regensburg, Department of Economics.
    8. Granger, Clive W J, 1986. "Developments in the Study of Cointegrated Economic Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 213-228, August.
    9. Johansen, Søren, 2010. "Some identification problems in the cointegrated vector autoregressive model," Journal of Econometrics, Elsevier, vol. 158(2), pages 262-273, October.
    10. 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.
    11. Hualde, Javier & Velasco, Carlos, 2008. "Distribution-Free Tests Of Fractional Cointegration," Econometric Theory, Cambridge University Press, vol. 24(1), pages 216-255, February.
    12. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February.
    13. Johansen, Søren, 1995. "A Stastistical Analysis of Cointegration for I(2) Variables," Econometric Theory, Cambridge University Press, vol. 11(1), pages 25-59, February.
    14. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    15. Nielsen, Morten Orregaard & Shimotsu, Katsumi, 2007. "Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 574-596, December.
    16. Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 67-77, September.
    17. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    18. Christensen, Bent Jesper & Nielsen, Morten Orregaard, 2006. "Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting," Journal of Econometrics, Elsevier, vol. 133(1), pages 343-371, July.
    19. Chen, Willa W. & Hurvich, Clifford M., 2003. "Semiparametric Estimation of Multivariate Fractional Cointegration," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 629-642, January.
    20. 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.
    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. Søren Johansen & Morten Ørregaard Nielsen, 2019. "Nonstationary Cointegration in the Fractionally Cointegrated VAR Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(4), pages 519-543, July.
    2. Federico Carlini & Paolo Santucci de Magistris, 2019. "Resuscitating the co-fractional model of Granger (1986)," CREATES Research Papers 2019-02, Department of Economics and Business Economics, Aarhus University.
    3. Søren Johansen & Morten Ørregaard Nielsen, 2018. "Testing the CVAR in the Fractional CVAR Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 836-849, November.
    4. 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.
    5. Mishra, Tapas & Park, Donghyun & Parhi, Mamata & Uddin, Gazi Salah & Tian, Shu, 2023. "A memory in the bond: Green bond and sectoral investment interdependence in a fractionally cointegrated VAR framework," Energy Economics, Elsevier, vol. 121(C).
    6. Sepideh Dolatabadi & Morten Ørregaard Nielsen & Ke Xu, 2015. "A Fractionally Cointegrated VAR Analysis of Price Discovery in Commodity Futures Markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 35(4), pages 339-356, April.
    7. Filippo Beltrami & Fulvio Fontini & Monica Giulietti & Luigi Grossi, 2022. "The Zonal and Seasonal CO2 Marginal Emissions Factors for the Italian Power Market," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 83(2), pages 381-411, October.
    8. Dolatabadi, Sepideh & Nielsen, Morten Ørregaard & Xu, Ke, 2016. "A fractionally cointegrated VAR model with deterministic trends and application to commodity futures markets," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 623-639.
    9. Håvard Hungnes, 2016. "Fractionality and co-fractionality between Government Bond yields," Discussion Papers 838, Statistics Norway, Research Department.
    10. Bent Jesper Christensen & Nabanita Datta Gupta & Paolo Santucci de Magistris, 2021. "Measuring the impact of clean energy production on CO2 abatement in Denmark: Upper bound estimation and forecasting," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(1), pages 118-149, January.
    11. Federico Carlini & Katarzyna Lasak, 2014. "On an Estimation Method for an Alternative Fractionally Cointegrated Model," Tinbergen Institute Discussion Papers 14-052/III, Tinbergen Institute.
    12. Forte, Santiago & Lovreta, Lidija, 2019. "Volatility discovery: Can the CDS market beat the equity options market?," Finance Research Letters, Elsevier, vol. 28(C), pages 107-111.
    13. 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.
    14. Massimiliano Caporin & Fulvio Fontini & Paolo Santucci De Magistris, 2017. "Price convergence within and between the Italian electricity day-ahead and dispatching services markets," "Marco Fanno" Working Papers 0215, Dipartimento di Scienze Economiche "Marco Fanno".
    15. Carlini, Federico & Christensen, Bent Jesper & Datta Gupta, Nabanita & Santucci de Magistris, Paolo, 2023. "Climate, wind energy, and CO2 emissions from energy production in Denmark," Energy Economics, Elsevier, vol. 125(C).
    16. Gustavo Fruet Dias & Cristina M. Scherrer & Fotis Papailias, 2016. "Volatility Discovery," CREATES Research Papers 2016-07, Department of Economics and Business Economics, Aarhus University.
    17. 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.

    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. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    2. Federico Carlini & Paolo Santucci de Magistris, 2019. "Resuscitating the co-fractional model of Granger (1986)," CREATES Research Papers 2019-02, Department of Economics and Business Economics, Aarhus University.
    3. Christian Leschinski & Michelle Voges & Philipp Sibbertsen, 2021. "A comparison of semiparametric tests for fractional cointegration," Statistical Papers, Springer, vol. 62(4), pages 1997-2030, August.
    4. 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.
    5. Katarzyna Łasak & Carlos Velasco, 2015. "Fractional Cointegration Rank Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 241-254, April.
    6. Demetrescu, Matei & Kusin, Vladimir & Salish, Nazarii, 2022. "Testing for no cointegration in vector autoregressions with estimated degree of fractional integration," Economic Modelling, Elsevier, vol. 108(C).
    7. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, Department of Economics and Business Economics, Aarhus University.
    8. Tobias Hartl & Roland Weigand, 2018. "Multivariate Fractional Components Analysis," Papers 1812.09149, arXiv.org, revised Jan 2019.
    9. Nielsen, Morten Ørregaard, 2010. "Nonparametric cointegration analysis of fractional systems with unknown integration orders," Journal of Econometrics, Elsevier, vol. 155(2), pages 170-187, April.
    10. Yaya, OlaOluwa S & Gil-Alana, Luis A., 2018. "High and Low Intraday Commodity Prices: A Fractional Integration and Cointegration Approach," MPRA Paper 90518, University Library of Munich, Germany.
    11. Dechert, Andreas, 2014. "Fraktionale Kointegrationsbeziehungen zwischen Euribor-Zinssätzen," W.E.P. - Würzburg Economic Papers 93, University of Würzburg, Department of Economics.
    12. Avarucci, Marco & Velasco, Carlos, 2009. "A Wald test for the cointegration rank in nonstationary fractional systems," Journal of Econometrics, Elsevier, vol. 151(2), pages 178-189, August.
    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. Hualde, J. & Robinson, P.M., 2010. "Semiparametric inference in multivariate fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 157(2), pages 492-511, August.
    15. Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 67-77, September.
    16. Pérez-Rodríguez, Jorge V. & Andrada-Félix, Julián & Rachinger, Heiko, 2021. "Testing the forward volatility unbiasedness hypothesis in exchange rates under long-range dependence," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    17. Galán-Gutiérrez, Juan Antonio & Martín-García, Rodrigo, 2021. "Cointegration between the structure of copper futures prices and Brexit," Resources Policy, Elsevier, vol. 71(C).
    18. Nielsen, Morten Orregaard & Shimotsu, Katsumi, 2007. "Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 574-596, December.
    19. Abakah, Emmanuel Joel Aikins & Caporale, Guglielmo Maria & Gil-Alana, Luis Alberiko, 2021. "Economic policy uncertainty: Persistence and cross-country linkages," Research in International Business and Finance, Elsevier, vol. 58(C).
    20. Dechert, Andreas, 2012. "Variance Ratio Testing for Fractional Cointegration in Presence of Trends and Trend Breaks," MPRA Paper 41044, University Library of Munich, Germany.

    More about this item

    Keywords

    Fractional Cointegration; Cofractional Models; Identification; Lag;
    All these keywords.

    JEL classification:

    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • 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:aah:create:2013-44. 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.econ.au.dk/afn/ .

    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.