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Likelihood based inference for an Identifiable Fractional Vector Error Correction Model

Author

Listed:
  • Federico Carlini

    (USI, Lugano)

  • Katarzyna (K.A.) Lasak

    (University of Amsterdam)

Abstract

We consider the Fractional Vector Error Correction model proposed in Avarucci (2007), which is characterized by a richer lag structure than the models proposed in Granger (1986) and Johansen (2008, 2009). In particular, we discuss the properties of the model of Avarucci (2007) (FECM) in comparison to the model of Johansen (2008, 2009) (FCVAR). Both models generate the same class of processes, but the properties of the two models are different. First, opposed to the model of Johansen (2008, 2009), the model of Avarucci has a convenient nesting structure, which allows for testing the number of lags and the cointegration rank exactly in the same way as in the standard I(1) cointegration framework of Johansen (1995) and hence might be attractive for econometric practice. Second, we find that the model of Avarucci (2007) is almost free from identification problems, contrary to the model of Johansen (2008, 2009) and Johansen and Nielsen (2012), which identification problems are discussed in Carlini and Santucci de Magistris (2017). However, due to a larger number of parameters, the estimation of the FECM model of Avarucci (2007) turns out to be more complicated. Therefore, we propose a 4-step estimation procedure for this model that is based on the switching algorithm employed in Carlini and Mosconi (2014), together with the GLS procedure of Mosconi and Paruolo (2014). We check the performance of the proposed estimation procedure in finite samples by means of a Monte Carlo experiment and we prove the asymptotic distribution of the estimators of all the parameters. The solution of the model has been previously derived in Avarucci (2007), while testing for the rank has been discussed in Lasak and Velasco (for cointegration strength >0.5) and Avarucci and Velasco (for cointegration strength

Suggested Citation

  • 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.
    • Handle: RePEc:tin:wpaper:20180085
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    References listed on IDEAS

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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. P. M. Robinson & J. Hualde, 2003. "Cointegration in Fractional Systems with Unknown Integration Orders," Econometrica, Econometric Society, vol. 71(6), pages 1727-1766, November.
    3. Michael Dueker & Richard Startz, 1998. "Maximum-Likelihood Estimation Of Fractional Cointegration With An Application To U.S. And Canadian Bond Rates," The Review of Economics and Statistics, MIT Press, vol. 80(3), pages 420-426, August.
    4. 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.
    5. 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.
    6. Hualde, Javier & Robinson, Peter M., 2003. "Cointegration in fractional systems with unkown integration orders," LSE Research Online Documents on Economics 58050, London School of Economics and Political Science, LSE Library.
    7. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    8. Mosconi, Rocco & Paruolo, Paolo, 2014. "Rank and order conditions for identification in simultaneous system of cointegrating equations with integrated variables of order two," MPRA Paper 53589, University Library of Munich, Germany.
    9. 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.
    10. Javier Hualde & Peter M Robinson, 2003. "Cointegration in Fractional Systems with Unkown Integration Orders," STICERD - Econometrics Paper Series 449, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    11. Robinson, Peter M. & Hualde, Javier, 2003. "Cointegration in fractional systems with unknown integration orders," LSE Research Online Documents on Economics 2223, London School of Economics and Political Science, LSE Library.
    12. 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.
    13. 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.
    14. Ignacio N. Lobato & Carlos Velasco, 2006. "Optimal Fractional Dickey-Fuller tests," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 492-510, November.
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    More about this item

    Keywords

    Error correction model; Gaussian VAR model; Fractional Cointegration; Estimation algorithm; Maximum likelihood estimation; Switching Algorithm; Reduced Rank Regression.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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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