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On the Identification of Fractionally Cointegrated VAR Models With the Condition

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  • Federico Carlini
  • Paolo Santucci de Magistris
Abstract
This article discusses identification problems in the fractionally cointegrated system of Johansen and Johansen and Nielsen. It is shown that several equivalent reparametrizations of the model associated with different fractional integration and cointegration parameters may exist for any choice of the lag-length when the true cointegration rank is known. The properties of these multiple nonidentified 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)$\mathcal {F}(d)$. This is a generalization of the well-known I(1) condition to the fractional case. Imposing a proper restriction on the fractional integration parameter, d, is sufficient to guarantee identification of all model parameters and the validity of the F(d)$\mathcal {F}(d)$ condition. The article also illustrates the indeterminacy between the cointegration rank and the lag-length. It is also proved that the model with rank zero and k lags may be an equivalent reparameterization of the model with full rank and k − 1 lags. This precludes the possibility to test for the cointegration rank unless a proper restriction on the fractional integration parameter is imposed.

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  • Federico Carlini & Paolo Santucci de Magistris, 2019. "On the Identification of Fractionally Cointegrated VAR Models With the Condition," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 134-146, January.
    • Handle: RePEc:taf:jnlbes:v:37:y:2019:i:1:p:134-146
    DOI: 10.1080/07350015.2017.1294077
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    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. 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.
    3. Katarzyna Łasak & Carlos Velasco, 2015. "Fractional Cointegration Rank Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 241-254, April.
    4. Johansen, Søren, 2010. "Some identification problems in the cointegrated vector autoregressive model," Journal of Econometrics, Elsevier, vol. 158(2), pages 262-273, October.
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    9. Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 67-77, September.
    10. 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.
    11. 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.
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    13. 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.
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    15. 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.
    16. 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.
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    20. 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.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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).
    7. 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.
    8. 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".
    9. Gustavo Fruet Dias & Cristina M. Scherrer & Fotis Papailias, 2016. "Volatility Discovery," CREATES Research Papers 2016-07, Department of Economics and Business Economics, Aarhus University.
    10. 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.
    11. 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.
    12. 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.
    13. 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).
    14. 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.
    15. Håvard Hungnes, 2016. "Fractionality and co-fractionality between Government Bond yields," Discussion Papers 838, Statistics Norway, Research Department.
    16. Federico Carlini & Katarzyna Lasak, 2014. "On an Estimation Method for an Alternative Fractionally Cointegrated Model," Tinbergen Institute Discussion Papers 14-052/III, Tinbergen Institute.
    17. 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.

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    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

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