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Testing the CVAR in the Fractional CVAR Model

Author

Listed:
  • Søren Johansen
  • Morten Ørregaard Nielsen

Abstract

We consider the fractional cointegrated vector autoregressive (CVAR) model of Johansen and Nielsen (2012a) and show that the likelihood ratio 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, 2018. "Testing the CVAR in the Fractional CVAR Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 836-849, November.
  • Handle: RePEc:bla:jtsera:v:39:y:2018:i:6:p:836-849
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    File URL: https://doi.org/10.1111/jtsa.12300
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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. 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(05), pages 1095-1139, October.
    3. 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.
    4. Johansen, Søren & Ørregaard Nielsen, Morten, 2012. "A Necessary Moment Condition For The Fractional Functional Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 28(03), pages 671-679, June.
    5. 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.
    6. 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.
    7. 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.
    8. Cathy Yi-Hsuan Chen & Thomas C. Chiang & Wolfgang Karl Härdle, 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 SFB649DP2016-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    9. 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.
    10. repec:taf:jnlbes:v:37:y:2019:i:1:p:134-146 is not listed on IDEAS
    11. 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.
    12. Johansen, SØren, 2008. "A Representation Theory For A Class Of Vector Autoregressive Models For Fractional Processes," Econometric Theory, Cambridge University Press, vol. 24(03), pages 651-676, June.
    13. 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.
    14. 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.
    15. 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.
    16. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August.
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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.

    More about this item

    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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