[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/qed/wpaper/1405.html
   My bibliography  Save this paper

Nonstationary Cointegration In The Fractionally Cointegrated Var Model

Author

Listed:
  • Morten Ø. Nielsen

    (Queen's University and CREATES)

  • S Johansen

    (University of Copenhagen 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 ?²-test.

Suggested Citation

  • Morten Ø. Nielsen & S Johansen, 2018. "Nonstationary Cointegration In The Fractionally Cointegrated Var Model," Working Paper 1405, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:1405
    as

    Download full text from publisher

    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/qed_wp_1405.pdf
    File Function: First version 2018
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    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 & Nielsen, Morten Ørregaard, 2010. "Likelihood inference for a nonstationary fractional autoregressive model," Journal of Econometrics, Elsevier, vol. 158(1), pages 51-66, September.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Wojciech Kopczuk, 2013. "Incentive Effects of Inheritances and Optimal Estate Taxation," American Economic Review, American Economic Association, vol. 103(3), pages 472-477, May.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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).
    4. 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.
    5. 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.
    6. 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.
    7. Javier Hualde & Morten {O}rregaard Nielsen, 2022. "Fractional integration and cointegration," Papers 2211.10235, arXiv.org.
    8. 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.
    9. 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).
    10. Hirukawa, Junichi & Raïssi, Hamdi, 2020. "Testing linear relationships between non-constant variances of economic variables," Economic Modelling, Elsevier, vol. 90(C), pages 182-189.
    11. 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.
    12. 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).
    13. 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).
    14. 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.
    15. 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).
    16. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    3. Nikolaos Stoupos & Apostolos Kiohos, 2022. "Euro Area: Towards a European Common Bond? – Empirical Evidence from the Sovereign Debt Markets," Journal of Common Market Studies, Wiley Blackwell, vol. 60(4), pages 1019-1046, July.
    4. 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).
    5. Yaya, OlaOluwa S & Gil-Alana, Luis A., 2018. "High and Low Intraday Commodity Prices: A Fractional Integration and Cointegration Approach," MPRA Paper 90518, University Library of Munich, Germany.
    6. Sepideh Dolatabadi & Paresh Kumar Narayan & Morten Ørregaard Nielsen & Ke Xu, 2018. "Economic significance of commodity return forecasts from the fractionally cointegrated VAR model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(2), pages 219-242, February.
    7. 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.
    8. Stoupos, Nikolaos & Kiohos, Apostolos, 2021. "Energy commodities and advanced stock markets: A post-crisis approach," Resources Policy, Elsevier, vol. 70(C).
    9. Alexander Boca Saravia & Gabriel Rodríguez, 2022. "Presidential approval in Peru: an empirical analysis using a fractionally cointegrated VAR," Economic Change and Restructuring, Springer, vol. 55(3), pages 1973-2010, August.
    10. Sepideh Dolatabadi & Morten Ørregaard Nielsen & Ke Xu, 2015. "A Fractionally Cointegrated VAR Analysis of Price Discovery in Commodity Futures Markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 35(4), pages 339-356, April.
    11. 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.
    12. 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).
    13. 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.
    14. 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).
    15. 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.
    16. Stoupos, Nikolaos & Kiohos, Apostolos, 2022. "Euro area stock markets integration: Empirical evidence after the end of 2010 debt crisis," Finance Research Letters, Elsevier, vol. 46(PB).
    17. 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).
    18. Filippo Beltrami & Fulvio Fontini & Monica Giulietti & Luigi Grossi, 2022. "The Zonal and Seasonal CO2 Marginal Emissions Factors for the Italian Power Market," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 83(2), pages 381-411, October.
    19. Samet Gunay, 2018. "Fractionally Cointegrated Vector Autoregression Model: Evaluation of High/Low and Close/Open Spreads for Precious Metals," SAGE Open, , vol. 8(4), pages 21582440188, November.
    20. 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.

    More about this item

    Keywords

    likelihood inference; fractional integration; cointegration; 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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:qed:wpaper:1405. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mark Babcock (email available below). General contact details of provider: https://edirc.repec.org/data/qedquca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.