IDEAS home Printed from https://ideas.repec.org/p/ces/ceswps/_7652.html
   My bibliography  Save this paper

High and low prices and the range in the European stock markets: a long-memory approach

Author

Listed:
  • Guglielmo Maria Caporale
  • Luis A. Gil-Alana
  • Carlos Poza

Abstract

This paper uses fractional integration techniques to examine the stochastic behaviour of high and low stock prices in Europe and then to test for the possible existence of long-run linkages between them by looking at the range, i.e., the difference between the two logged series. Specifically, monthly, weekly and daily data on the following five European stock market indices are analysed: DAX30 (Germany), FTSE100 (UK), CAC40 (France), FTSE MIB40 (Italy) and IBEX35 (Spain). In all cases, the order of integration of the range is lower than that of the original series, which implies the existence of a long-run equilibrium relationship between high and low prices. Further, the estimated fractional differencing parameter is positive in all cases, which represents evidence of long memory.

Suggested Citation

  • Guglielmo Maria Caporale & Luis A. Gil-Alana & Carlos Poza, 2019. "High and low prices and the range in the European stock markets: a long-memory approach," CESifo Working Paper Series 7652, CESifo.
    • Handle: RePEc:ces:ceswps:_7652
    as

    Download full text from publisher

    File URL: https://www.cesifo.org/DocDL/cesifo1_wp7652.pdf
    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. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    3. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    4. Garman, Mark B & Klass, Michael J, 1980. "On the Estimation of Security Price Volatilities from Historical Data," The Journal of Business, University of Chicago Press, vol. 53(1), pages 67-78, January.
    5. Philipp Sibbertsen, 2004. "Long memory versus structural breaks: An overview," Statistical Papers, Springer, vol. 45(4), pages 465-515, October.
    6. Lahiani, A. & Scaillet, O., 2009. "Testing for threshold effect in ARFIMA models: Application to US unemployment rate data," International Journal of Forecasting, Elsevier, vol. 25(2), pages 418-428.
    7. 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.
    8. Baillie, Richard T. & Morana, Claudio, 2009. "Modelling long memory and structural breaks in conditional variances: An adaptive FIGARCH approach," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1577-1592, August.
    9. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
    10. Chatzikonstanti, Vasiliki & Venetis, Ioannis A., 2015. "Long memory in log-range series: Do structural breaks matter?," Journal of Empirical Finance, Elsevier, vol. 33(C), pages 104-113.
    11. Diebold, Francis X. & Rudebusch, Glenn D., 1991. "On the power of Dickey-Fuller tests against fractional alternatives," Economics Letters, Elsevier, vol. 35(2), pages 155-160, February.
    12. Lee, Dongin & Schmidt, Peter, 1996. "On the power of the KPSS test of stationarity against fractionally-integrated alternatives," Journal of Econometrics, Elsevier, vol. 73(1), pages 285-302, July.
    13. Yang, Dennis & Zhang, Qiang, 2000. "Drift-Independent Volatility Estimation Based on High, Low, Open, and Close Prices," The Journal of Business, University of Chicago Press, vol. 73(3), pages 477-491, July.
    14. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
    15. Choi, Kyongwook & Yu, Wei-Choun & Zivot, Eric, 2010. "Long memory versus structural breaks in modeling and forecasting realized volatility," Journal of International Money and Finance, Elsevier, vol. 29(5), pages 857-875, September.
    16. 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.
    17. Granger, Clive W. J. & Hyung, Namwon, 2004. "Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 399-421, June.
    18. Luis A. Gil‐Alana, 2008. "Fractional integration and structural breaks at unknown periods of time," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 163-185, January.
    19. Chambers, Marcus J, 1998. "Long Memory and Aggregation in Macroeconomic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1053-1072, November.
    20. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2007. "Nonstationarity-extended local Whittle estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1353-1384, December.
    21. Yan-Leung Cheung & Yin-Wong Cheung & Alan T. K. Wan, 2009. "A high-low model of daily stock price ranges," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(2), pages 103-119.
    22. Cioczek-Georges, R. & Mandelbrot, B. B., 1995. "A class of micropulses and antipersistent fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 1-18, November.
    23. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    24. Yin-Wong Cheung, 2007. "An empirical model of daily highs and lows," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 12(1), pages 1-20.
    25. Davidson, James & Terasvirta, Timo, 2002. "Long memory and nonlinear time series," Journal of Econometrics, Elsevier, vol. 110(2), pages 105-112, October.
    26. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    27. Al-Shboul, Mohammad & Anwar, Sajid, 2016. "Fractional integration in daily stock market indices at Jordan's Amman stock exchange," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 16-37.
    28. Zaffaroni, Paolo, 2004. "Contemporaneous aggregation of linear dynamic models in large economies," Journal of Econometrics, Elsevier, vol. 120(1), pages 75-102, May.
    29. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
    30. Angela He & Alan Wan, 2009. "Predicting daily highs and lows of exchange rates: a cointegration analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(11), pages 1191-1204.
    31. Granger, Clive W J, 1986. "Developments in the Study of Cointegrated Economic Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 213-228, August.
    32. 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.
    33. Eunju Hwang & Dong Wan Shin, 2018. "Tests for structural breaks in memory parameters of long-memory heterogeneous autoregressive models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(21), pages 5378-5389, November.
    34. Taylor, Mark P. & Allen, Helen, 1992. "The use of technical analysis in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 11(3), pages 304-314, June.
    35. Fiess, Norbert M & MacDonald, Ronald, 2002. "Towards the fundamentals of technical analysis: analysing the information content of High, Low and Close prices," Economic Modelling, Elsevier, vol. 19(3), pages 353-374, May.
    36. 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.
    37. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    38. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    39. Hassler, Uwe & Wolters, Jurgen, 1994. "On the power of unit root tests against fractional alternatives," Economics Letters, Elsevier, vol. 45(1), pages 1-5, May.
    40. Georges Oppenheim & Marie‐Claude Viano, 2004. "Aggregation of random parameters Ornstein‐Uhlenbeck or AR processes: some convergence results," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(3), pages 335-350, May.
    41. William R. Parke, 1999. "What Is Fractional Integration?," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 632-638, November.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    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. Javier Hualde & Morten {O}rregaard Nielsen, 2022. "Fractional integration and cointegration," Papers 2211.10235, arXiv.org.
    4. 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.
    5. Leandro Maciel, 2020. "Technical analysis based on high and low stock prices forecasts: evidence for Brazil using a fractionally cointegrated VAR model," Empirical Economics, Springer, vol. 58(4), pages 1513-1540, April.
    6. Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 1-34.
    7. 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.
    8. Aye, Goodness C. & Carcel, Hector & Gil-Alana, Luis A. & Gupta, Rangan, 2017. "Does gold act as a hedge against inflation in the UK? Evidence from a fractional cointegration approach over 1257 to 2016," Resources Policy, Elsevier, vol. 54(C), pages 53-57.
    9. Kunal Saha & Vinodh Madhavan & Chandrashekhar G. R. & David McMillan, 2020. "Pitfalls in long memory research," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1733280-173, January.
    10. repec:got:cegedp:76 is not listed on IDEAS
    11. Michael KUEHL, 2008. "Strong Comovements of Exchange Rates: Theoretical and Empirical Cases when Currencies Become the Same Asset," EcoMod2008 23800071, EcoMod.
    12. Aikins Abakah, Emmanuel Joel & Gil-Alana, Luis A. & Tripathy, Trilochan, 2022. "Stochastic structure of metal prices: Evidence from fractional integration non-linearities and breaks," Resources Policy, Elsevier, vol. 78(C).
    13. Caporale, Guglielmo Maria & Gil-Alana, Luis A., 2008. "Modelling the US, UK and Japanese unemployment rates: Fractional integration and structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4998-5013, July.
    14. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2020. "Modelling Loans to Non-Financial Corporations within the Eurozone: A Long-Memory Approach," CESifo Working Paper Series 8674, CESifo.
    15. OlaOluwa S. Yaya & Xuan Vinh Vo & Ahamuefula E. Ogbonna & Adeolu O. Adewuyi, 2022. "Modelling cryptocurrency high–low prices using fractional cointegrating VAR," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(1), pages 489-505, January.
    16. Guglielmo Maria Caporale & Luis Gil‐Alana, 2014. "Long‐Run and Cyclical Dynamics in the US Stock Market," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(2), pages 147-161, March.
    17. Monge, Manuel & Romero Rojo, María Fátima & Gil-Alana, Luis Alberiko, 2023. "The impact of geopolitical risk on the behavior of oil prices and freight rates," Energy, Elsevier, vol. 269(C).
    18. Guglielmo Maria Caporale & Luis A. Gil‐Alana & James C. Orlando, 2016. "Linkages Between the US and European Stock Markets: A Fractional Cointegration Approach," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 21(2), pages 143-153, April.
    19. Gil-Alana, Luis Alberiko & Dettoni, Robinson & Costamagna, Rodrigo & Valenzuela, Mario, 2019. "Rational bubbles in the real housing stock market: Empirical evidence from Santiago de Chile," Research in International Business and Finance, Elsevier, vol. 49(C), pages 269-281.
    20. Abakah, Emmanuel Joel Aikins & Caporale, Guglielmo Maria & Gil-Alana, Luis Alberiko, 2021. "Economic policy uncertainty: Persistence and cross-country linkages," Research in International Business and Finance, Elsevier, vol. 58(C).
    21. Jose Maria Fernandez-Crehuet & Luis Alberiko Gil-Alana & Cristina Martí Barco, 2020. "Unemployment and Fertility: A Long Run Relationship," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 152(3), pages 1177-1196, December.

    More about this item

    Keywords

    high and low prices; range; fractional integration;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

    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:ces:ceswps:_7652. 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: Klaus Wohlrabe (email available below). General contact details of provider: https://edirc.repec.org/data/cesifde.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.