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Testing the CVAR in the fractional CVAR model

Author

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  • Søren Johansen

    (University of Copenhagen and CREATES)

  • Morten Ørregaard Nielsen

    (Queen's University and CREATES)

Abstract

We consider the fractional cointegrated vector autoregressive (CVAR) model of Johansen and Nielsen (2012a) and show that the test statistic for the usual CVAR model is asymptotically chi-squared distributed. Because the usual CVAR model lies on the boundary of the parameter space for the fractional CVAR in Johansen and Nielsen (2012a), the analysis requires the study of the fractional CVAR model on a slightly larger parameter space so that the CVAR model lies in the interior. This in turn implies some further analysis of the asymptotic properties of the fractional CVAR model.

Suggested Citation

  • Søren Johansen & Morten Ørregaard Nielsen, 2017. "Testing the CVAR in the fractional CVAR model," CREATES Research Papers 2017-37, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2017-37
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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. 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.
    3. Andreas Noack Jensen & Morten Ørregaard Nielsen, 2014. "A Fast Fractional Difference Algorithm," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 428-436, August.
    4. Johansen, Søren & Nielsen, Morten Ørregaard, 2016. "The Role Of Initial Values In Conditional Sum-Of-Squares Estimation Of Nonstationary Fractional Time Series Models," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1095-1139, October.
    5. Johansen, Søren & Ørregaard Nielsen, Morten, 2012. "A Necessary Moment Condition For The Fractional Functional Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 28(3), pages 671-679, June.
    6. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    7. Juan J. Dolado & Jesus Gonzalo & Laura Mayoral, 2002. "A Fractional Dickey-Fuller Test for Unit Roots," Econometrica, Econometric Society, vol. 70(5), pages 1963-2006, September.
    8. 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.
    9. Morten Ørregaard Nielsen & Michał Ksawery Popiel, 2018. "A Matlab program and user's guide for the fractionally cointegrated VAR model," Working Papers 1330, Queen's University, Department of Economics.
    10. 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.
    11. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(4), pages 549-582, August.
    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. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
    14. Christos Agiakloglou & Paul Newbold, 1994. "Lagrange Multiplier Tests For Fractional Difference," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(3), pages 253-262, May.
    15. Bollerslev, Tim & Osterrieder, Daniela & Sizova, Natalia & Tauchen, George, 2013. "Risk and return: Long-run relations, fractional cointegration, and return predictability," Journal of Financial Economics, Elsevier, vol. 108(2), pages 409-424.
    16. 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.
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    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.
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    5. Yan, Meng & Chen, Jian & Song, Victor & Xu, Ke, 2022. "Trade friction and price discovery in the USD–CAD spot and forward markets," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    6. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    7. Stoupos, Nikolaos & Kiohos, Apostolos, 2022. "Bond markets integration in the EU: New empirical evidence from the Eastern non-euro member-states," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    8. 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.
    9. Xu, Ke & Stewart, Kenneth G. & Cao, Zeyang, 2022. "Fractional cointegration and price discovery in Canadian commodities," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    10. Abbritti, Mirko & Carcel, Hector & Gil-Alana, Luis & Moreno, Antonio, 2023. "Term premium in a fractionally cointegrated yield curve," Journal of Banking & Finance, Elsevier, vol. 149(C).
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    12. Carlos D. Ramirez, 2024. "The effect of economic policy uncertainty under fractional integration," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 23(1), pages 89-110, January.

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    More about this item

    Keywords

    Cointegration; fractional integration; likelihood inference; vector autoregressive model;
    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

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