IDEAS home Printed from https://ideas.repec.org/p/zbw/iwqwdp/112015.html
   My bibliography  Save this paper

On the power and size properties of cointegration tests in the light of high-frequency stylized facts

Author

Listed:
  • Krauss, Christopher
  • Herrmann, Klaus
  • Teis, Stefan

Abstract

This paper first establishes a selection of stylized facts for high-frequency cointegration processes in the European equity market. Empirical evidence is given by one minute-binned transaction data of all DAX 30 constituents as traded on Deutsche Börse's Xetra market in 2014. A methodology is introduced to simulate cointegrated stock pairs, following none, some or all of the discussed stylized facts. In particular, AR(1), AR(1)-GARCH(1,1) and multiple regime STAR(1)-GARCH(1,1) processes are used to model the cointegration relationship. Furthermore, this cointegration relationship is contaminated with jumps. Based on these processes, the power and size properties of ten contemporary cointegration tests are assessed. We provide an economic interpretation of our approach by relating cointegration to relative-value arbitrage strategies in near-efficient markets. Quintessentially, we find that in a high-frequency setting typical for stock price data, selected cointegration tests still exhibit high power. Especially the Phillips-Perron and the Pantula, Gonzalez-Farias and Fuller tests perform best at very limited size distortions.

Suggested Citation

  • Krauss, Christopher & Herrmann, Klaus & Teis, Stefan, 2015. "On the power and size properties of cointegration tests in the light of high-frequency stylized facts," FAU Discussion Papers in Economics 11/2015, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    • Handle: RePEc:zbw:iwqwdp:112015
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/120866/1/835959325.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Balke, Nathan S & Fomby, Thomas B, 1997. "Threshold Cointegration," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 627-645, August.
    2. Hansen, Bruce E. & Seo, Byeongseon, 2002. "Testing for two-regime threshold cointegration in vector error-correction models," Journal of Econometrics, Elsevier, vol. 110(2), pages 293-318, October.
    3. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 1-30.
    4. Pratap Chandra Pati & Prabina Rajib, 2011. "Intraday return dynamics and volatility spillovers between NSE S&P CNX Nifty stock index and stock index futures," Applied Economics Letters, Taylor & Francis Journals, vol. 18(6), pages 567-574.
    5. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
    6. Sokbae Lee & Myung Hwan Seo & Youngki Shin, 2017. "Correction," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 883-883, April.
    7. Haug, Alfred A., 1996. "Tests for cointegration a Monte Carlo comparison," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 89-115.
    8. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    9. Perron, Pierre, 1988. "Trends and random walks in macroeconomic time series : Further evidence from a new approach," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 297-332.
    10. Chen, Zhiwu & Knez, Peter J, 1995. "Measurement of Market Integration and Arbitrage," The Review of Financial Studies, Society for Financial Studies, vol. 8(2), pages 287-325.
    11. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 247-318.
    12. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Cointegration Rank Testing Under Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1719-1760, December.
    13. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    14. Dijk, Dick van & Franses, Philip Hans, 1999. "Modeling Multiple Regimes in the Business Cycle," Macroeconomic Dynamics, Cambridge University Press, vol. 3(3), pages 311-340, September.
    15. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    16. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    17. Evan Gatev & William N. Goetzmann & K. Geert Rouwenhorst, 2006. "Pairs Trading: Performance of a Relative-Value Arbitrage Rule," The Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 797-827.
    18. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Testing for co-integration in vector autoregressions with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 158(1), pages 7-24, September.
    19. Jurgen A. Doornik, 1998. "Approximations To The Asymptotic Distributions Of Cointegration Tests," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 573-593, December.
    20. Kremers, Jeroen J M & Ericsson, Neil R & Dolado, Juan J, 1992. "The Power of Cointegration Tests," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 325-348, August.
    21. Robert F. Engle & Magdalena E. Sokalska, 0. "Forecasting intraday volatility in the US equity market. Multiplicative component GARCH," Journal of Financial Econometrics, Oxford University Press, vol. 10(1), pages 54-83.
    22. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    23. Krauss, Christopher, 2015. "Statistical arbitrage pairs trading strategies: Review and outlook," FAU Discussion Papers in Economics 09/2015, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    24. Pantula, Sastry G & Gonzalez-Farias, Graciela & Fuller, Wayne A, 1994. "A Comparison of Unit-Root Test Criteria," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 449-459, October.
    25. Elyasiani, Elyas & Kocagil, Ahmet E., 2001. "Interdependence and dynamics in currency futures markets: A multivariate analysis of intraday data," Journal of Banking & Finance, Elsevier, vol. 25(6), pages 1161-1186, June.
    26. Joel Hasbrouck, 2003. "Intraday Price Formation in U.S. Equity Index Markets," Journal of Finance, American Finance Association, vol. 58(6), pages 2375-2400, December.
    27. Breitung, Jorg & Taylor, A. M. Robert, 2003. "Corrigendum to "Nonparametric tests for unit roots and cointegration" [J. Econom. 108 (2002) 343-363]," Journal of Econometrics, Elsevier, vol. 117(2), pages 401-404, December.
    28. repec:bla:jecsur:v:12:y:1998:i:5:p:573-93 is not listed on IDEAS
    29. H. Peter Boswijk & Andre Lucas & Nick Taylor, 1999. "A Comparison of Parametric, Semi-nonparametric, Adaptive, and Nonparametric Cointegration Tests," Tinbergen Institute Discussion Papers 99-012/4, Tinbergen Institute.
    30. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    31. Herrmann, Klaus & Teis, Stefan & Yu, Weijun, 2014. "Components of intraday volatility and their prediction at different sampling frequencies with application to DAX and BUND futures," FAU Discussion Papers in Economics 15/2014, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    32. Schmidt, Peter & Phillips, C B Peter, 1992. "LM Tests for a Unit Root in the Presence of Deterministic Trends," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 257-287, August.
    33. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
    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. Clegg, Matthew & Krauss, Christopher, 2016. "Pairs trading with partial cointegration," FAU Discussion Papers in Economics 05/2016, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.

    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. Christopher Krauss & Klaus Herrmann, 2017. "On the Power and Size Properties of Cointegration Tests in the Light of High-Frequency Stylized Facts," JRFM, MDPI, vol. 10(1), pages 1-24, February.
    2. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 247-318.
    3. Clegg, Matthew & Krauss, Christopher, 2016. "Pairs trading with partial cointegration," FAU Discussion Papers in Economics 05/2016, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    4. Mohcine Bakhat & Klaas WŸrzburg, 2013. "Co-integration of Oil and Commodity Prices: A Comprehensive ApproachAbstract," Working Papers fa05-2013, Economics for Energy.
    5. Neil R. Ericsson & James G. MacKinnon, 2002. "Distributions of error correction tests for cointegration," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 285-318, June.
    6. Aamir Jamal & G. M. Bhat, 2023. "Disentangling the Nexus Between Exchange Rate Volatility, Exports, and FDI: Empirical Evidence from the Indian Economy," Global Journal of Emerging Market Economies, Emerging Markets Forum, vol. 15(3), pages 449-472, September.
    7. Kanjilal, Kakali & Ghosh, Sajal, 2017. "Dynamics of crude oil and gold price post 2008 global financial crisis – New evidence from threshold vector error-correction model," Resources Policy, Elsevier, vol. 52(C), pages 358-365.
    8. Committee, Nobel Prize, 2003. "Time-series Econometrics: Cointegration and Autoregressive Conditional Heteroskedasticity," Nobel Prize in Economics documents 2003-1, Nobel Prize Committee.
    9. Al-Sadoon, Majid M., 2017. "A unifying theory of tests of rank," Journal of Econometrics, Elsevier, vol. 199(1), pages 49-62.
    10. Huo, Rui & Ahmed, Abdullahi D., 2018. "Relationships between Chinese stock market and its index futures market: Evaluating the impact of QFII scheme," Research in International Business and Finance, Elsevier, vol. 44(C), pages 135-152.
    11. Gary Cornwall & Jeff Chen & Beau Sauley, 2021. "Standing on the Shoulders of Machine Learning: Can We Improve Hypothesis Testing?," Papers 2103.01368, arXiv.org.
    12. Balsalobre-Lorente, Daniel & Bekun, Festus Victor & Etokakpan, Mfonobong Udom & Driha, Oana M., 2019. "A road to enhancements in natural gas use in Iran: A multivariate modelling approach," Resources Policy, Elsevier, vol. 64(C).
    13. Osamah M. Al-Khazali, 2003. "Stock Prices, Inflation, and Output: Evidence from the Emerging Markets," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 2(3), pages 287-314, September.
    14. Emmanouil Mavrakis & Christos Alexakis, 2018. "Statistical Arbitrage Strategies under Different Market Conditions: The Case of the Greek Banking Sector," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 17(2), pages 159-185, August.
    15. Sahito, Jam Ghulam Murtaza, 2015. "Market integration of wheat in Pakistan," Discussion Papers 72, Justus Liebig University Giessen, Center for international Development and Environmental Research (ZEU).
    16. Erdal Demirhan & Banu Demirhan, 2015. "The Dynamic Effect of ExchangeRate Volatility on Turkish Exports: Parsimonious Error-Correction Model Approach," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 62(4), pages 429-451, September.
    17. Campos, Julia & Ericsson, Neil R. & Hendry, David F., 1996. "Cointegration tests in the presence of structural breaks," Journal of Econometrics, Elsevier, vol. 70(1), pages 187-220, January.
    18. Norah Al-Ballaa, 2005. "Test for cointegration based on two-stage least squares," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 707-713.
    19. Ricardo Ferraz & Joaquim Miranda Sarmento & António Portugal Duarte, 2024. "The Sustainability of Portuguese Fiscal Policy in Democracy, 1974–2020," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 22(3), pages 749-772, September.
    20. Mcgibany, James M. & Nourzad, Farrokh, 1995. "Exchange rate volatility and the demand for money in the U.S," International Review of Economics & Finance, Elsevier, vol. 4(4), pages 411-425.

    More about this item

    Keywords

    cointegration testing; high-frequency; stylized facts; power analysis; conditional heteroskedasticity; smooth transition autoregressive models;
    All these keywords.

    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:zbw:iwqwdp:112015. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/vierlde.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.