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Nonstationary cointegration in the fractionally cointegrated VAR 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 make two distinct contributions. First, in their consistency proof, Johansen and Nielsen (2012a) imposed moment conditions on the errors that depend on the parameter space, such that when the parameter space is larger, stronger moment conditions are required. We show that these moment conditions can be relaxed, and for consistency we require just eight moments regardless of the parameter space. Second, Johansen and Nielsen (2012a) assumed that the cointegrating vectors are stationary, and we extend the analysis to include the possibility that the cointegrating vectors are nonstationary. Both contributions require new analysis and results for the asymptotic properties of the likelihood function of the fractional CVAR model, which we provide. Finally, our analysis follows recent research and applies a parameter space large enough that the usual (non-fractional) CVAR model constitutes an interior point and hence can be tested against the fractional model using a khi2-test.

Suggested Citation

  • Søren Johansen & Morten Ørregaard Nielsen, 2018. "Nonstationary cointegration in the fractionally cointegrated VAR model," CREATES Research Papers 2018-17, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2018-17
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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. Emmanuel Saez & Joel Slemrod & Seth H. Giertz, 2012. "The Elasticity of Taxable Income with Respect to Marginal Tax Rates: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 50(1), pages 3-50, March.
    5. 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.
    6. Caporin, Massimiliano & Ranaldo, Angelo & Santucci de Magistris, Paolo, 2013. "On the predictability of stock prices: A case for high and low prices," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5132-5146.
    7. 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.
    8. 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.
    9. Baruník, Jozef & Dvořáková, Sylvie, 2015. "An empirical model of fractionally cointegrated daily high and low stock market prices," Economic Modelling, Elsevier, vol. 45(C), pages 193-206.
    10. 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.
    11. Emmanuel Saez & Gabriel Zucman, 2016. "Editor's Choice Wealth Inequality in the United States since 1913: Evidence from Capitalized Income Tax Data," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(2), pages 519-578.
    12. 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.
    13. Wojciech Kopczuk, 2013. "Incentive Effects of Inheritances and Optimal Estate Taxation," American Economic Review, American Economic Association, vol. 103(3), pages 472-477, May.
    14. David Seim, 2017. "Behavioral Responses to Wealth Taxes: Evidence from Sweden," American Economic Journal: Economic Policy, American Economic Association, vol. 9(4), pages 395-421, November.
    15. Morten Ø. Nielsen & Michal Ksawery Popiel, 2018. "A Matlab Program And User's Guide For The Fractionally Cointegrated Var Model," Working Paper 1330, Economics Department, Queen's University.
    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. Yao, Xingzhi & Izzeldin, Marwan & Li, Zhenxiong, 2019. "Modelling systems with a mixture of I(d) and I(0) variables using the fractionally co-integrated VAR model," Economics Letters, Elsevier, vol. 181(C), pages 160-163.
    2. Pérez-Rodríguez, Jorge V. & Andrada-Félix, Julián & Rachinger, Heiko, 2021. "Testing the forward volatility unbiasedness hypothesis in exchange rates under long-range dependence," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    3. Alia Afzal & Philipp Sibbertsen, 2021. "Modeling fractional cointegration between high and low stock prices in Asian countries," Empirical Economics, Springer, vol. 60(2), pages 661-682, February.
    4. 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).
    5. Hualde, Javier & Nielsen, Morten Ørregaard, 2020. "Truncated Sum Of Squares Estimation Of Fractional Time Series Models With Deterministic Trends," Econometric Theory, Cambridge University Press, vol. 36(4), pages 751-772, August.
    6. Xu, Ke & Chen, Yu-Lun & Yang, J. Jimmy, 2023. "Market uncertainty, persistent arbitrage-free violation, and price discovery in RMB market," International Review of Financial Analysis, Elsevier, vol. 90(C).
    7. Quineche Ricardo, 2021. "Consumption, Aggregate Wealth and Expected Stock Returns: An FCVAR Approach," Journal of Time Series Econometrics, De Gruyter, vol. 13(1), pages 21-42, January.
    8. Ke Xu & Yu‐Lun Chen & Bo Liu & Jian Chen, 2024. "Price discovery and long‐memory property: Simulation and empirical evidence from the bitcoin market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(4), pages 605-618, April.
    9. Christian Leschinski & Michelle Voges & Philipp Sibbertsen, 2021. "A comparison of semiparametric tests for fractional cointegration," Statistical Papers, Springer, vol. 62(4), pages 1997-2030, August.
    10. Javier Hualde & Morten {O}rregaard Nielsen, 2022. "Fractional integration and cointegration," Papers 2211.10235, arXiv.org.
    11. Ataei, Masoud & Chen, Shengyuan & Yang, Zijiang & Peyghami, M. Reza, 2021. "Theory and applications of financial chaos index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    12. Javier Hualde & Morten Ørregaard Nielsen, 2022. "Truncated sum-of-squares estimation of fractional time series models with generalized power law trend," CREATES Research Papers 2022-07, Department of Economics and Business Economics, Aarhus University.
    13. 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.
    14. Chen, Yu-Lun & Xu, Ke, 2021. "The impact of RMB’s SDR inclusion on price discovery in onshore-offshore markets," Journal of Banking & Finance, Elsevier, vol. 127(C).
    15. Hirukawa, Junichi & Raïssi, Hamdi, 2020. "Testing linear relationships between non-constant variances of economic variables," Economic Modelling, Elsevier, vol. 90(C), pages 182-189.
    16. 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.
    17. Jayawardena, Nirodha I. & Todorova, Neda & Li, Bin & Su, Jen-Je & Gau, Yin-Feng, 2022. "Risk-return trade-off in the Australian Securities Exchange: Accounting for overnight effects, realized higher moments, long-run relations, and fractional cointegration," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 384-401.

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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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