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Testing the CVAR in the Fractional CVAR Model

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  • 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
    DOI: 10.1111/jtsa.12300
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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. 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.
    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. 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.
    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.
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    8. 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.
    9. 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.
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    5. 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.
    6. 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.
    7. 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).
    8. 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).
    9. Javier Hualde & Morten {O}rregaard Nielsen, 2022. "Fractional integration and cointegration," Papers 2211.10235, arXiv.org.
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    12. 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).

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    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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