[go: up one dir, main page]

IDEAS home Printed from https://ideas.repec.org/p/una/unccee/wp1503.html
   My bibliography  Save this paper

Testing of Nonstationary Cycles in Financial Time Series Data

Author

Listed:
  • Javier De Peña
  • Luis A. Gil-Alana

    (School of Economics and Business Administration, University of Navarra)

Abstract
In this article we propose a new method for testing nonstationary cycles in financial time series data. In particular, we use a procedure due to Robinson (1994) that permits us to test unit root cycles in raw time series. These tests have several distinguishing features compared with other procedures. In particular, they have a standard null limit distribution and they are the most efficient ones when directed against the appropriate alternatives. In addition, the procedure of Robinson (1994) allows us to test unit root cycles at each of the frequencies, and thus permits us to approximate the number of periods per cycle. The results, based on the daily structure of the Spanish stock market prices (IBEX 35) show that some intra-year cycles occur, and they take place at approximately 6, 9 or between 24 and 50 periods.

Suggested Citation

  • Javier De Peña & Luis A. Gil-Alana, 2003. "Testing of Nonstationary Cycles in Financial Time Series Data," Faculty Working Papers 15/03, School of Economics and Business Administration, University of Navarra.
  • Handle: RePEc:una:unccee:wp1503
    as

    Download full text from publisher

    File URL: http://www.unav.edu/documents/10174/6546776/1132241293_wp1503.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Keim, Donald B & Stambaugh, Robert F, 1984. "A Further Investigation of the Weekend Effect in Stock Returns," Journal of Finance, American Finance Association, vol. 39(3), pages 819-835, July.
    2. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    3. Chris Brooks & Melvin. J. Hinich & Douglas M. Patterson, 2003. "Intra-day Patterns in the Returns, Bidask Spereads, and Trading Volume of Stocks Traded on the New York Stock Exchange," ICMA Centre Discussion Papers in Finance icma-dp2003-14, Henley Business School, University of Reading.
    4. Carlos Forner & Joaquín Marhuenda, 2003. "Contrarian and Momentum Strategies in the Spanish Stock Market," European Financial Management, European Financial Management Association, vol. 9(1), pages 67-88, March.
    5. Arteche, Josu & Robinson, Peter M., 1998. "Seasonal and cyclical long memory," LSE Research Online Documents on Economics 2241, London School of Economics and Political Science, LSE Library.
    6. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    7. Bauwens, Luc & Ben Omrane, Walid & Giot, Pierre, 2005. "News announcements, market activity and volatility in the euro/dollar foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 24(7), pages 1108-1125, November.
    8. Bierens, Herman J., 2001. "Complex Unit Roots And Business Cycles: Are They Real?," Econometric Theory, Cambridge University Press, vol. 17(5), pages 962-983, October.
    9. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
    10. Juha Ahtola & George C. Tiao, 1987. "Distributions Of Least Squares Estimators Of Autoregressive Parameters For A Process With Complex Roots On The Unit Circle," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(1), pages 1-14, January.
    11. Andersen, Torben G & Bollerslev, Tim, 1997. "Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," Journal of Finance, American Finance Association, vol. 52(3), pages 975-1005, July.
    12. Joao F. Gomes & Amir Yaron & Lu Zhang, 2003. "Asset Prices and Business Cycles with Costly External Finance," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 767-788, October.
    13. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
    14. Kothari, S. P. & Shanken, Jay, 1997. "Book-to-market, dividend yield, and expected market returns: A time-series analysis," Journal of Financial Economics, Elsevier, vol. 44(2), pages 169-203, May.
    15. Melvin, Michael & Yin, Xixi, 2000. "Public Information Arrival, Exchange Rate Volatility, and Quote Frequency," Economic Journal, Royal Economic Society, vol. 110(465), pages 644-661, July.
    16. Josu Arteche & Peter M. Robinson, 2000. "Semiparametric Inference in Seasonal and Cyclical Long Memory Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(1), pages 1-25, January.
    17. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
    18. L. A. Gil-Alana & P. M. Robinson, 2001. "Testing of seasonal fractional integration in UK and Japanese consumption and income," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(2), pages 95-114.
    19. John Y. Campbell, Robert J. Shiller, 1988. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," The Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 195-228.
    20. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    21. Rogalski, Richard J, 1984. "A Further Investigation of the Weekend Effect in Stock Returns," Journal of Finance, American Finance Association, vol. 39(3), pages 835-837, July.
    22. Campbell, John Y., 1987. "Stock returns and the term structure," Journal of Financial Economics, Elsevier, vol. 18(2), pages 373-399, June.
    23. Muller, Ulrich A. & Dacorogna, Michel M. & Dave, Rakhal D. & Olsen, Richard B. & Pictet, Olivier V. & von Weizsacker, Jacob E., 1997. "Volatilities of different time resolutions -- Analyzing the dynamics of market components," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 213-239, June.
    24. Paolo Zaffaroni & Peter M. Robinson, 1997. "Nonlinear Time Series With Long Memory: A Model for Stochastic Volatility," FMG Discussion Papers dp253, Financial Markets Group.
    25. Gregory Mankiw, N. & Shapiro, Matthew D., 1986. "Do we reject too often? : Small sample properties of tests of rational expectations models," Economics Letters, Elsevier, vol. 20(2), pages 139-145.
    26. Lewellen, Jonathan, 2004. "Predicting returns with financial ratios," Journal of Financial Economics, Elsevier, vol. 74(2), pages 209-235, November.
    27. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415, September.
    28. Smirlock, Michael & Starks, Laura, 1986. "Day-of-the-week and intraday effects in stock returns," Journal of Financial Economics, Elsevier, vol. 17(1), pages 197-210, September.
    29. French, Kenneth R., 1980. "Stock returns and the weekend effect," Journal of Financial Economics, Elsevier, vol. 8(1), pages 55-69, March.
    30. Rogalski, Richard J, 1984. "New Findings Regarding Day-of-the-Week Returns over Trading and Non-trading Periods: A Note," Journal of Finance, American Finance Association, vol. 39(5), pages 1603-1614, December.
    31. Gregoir, Stéphane, 1999. "Multivariate Time Series With Various Hidden Unit Roots, Part Ii," Econometric Theory, Cambridge University Press, vol. 15(4), pages 469-518, August.
    32. Fama, Eugene F. & French, Kenneth R., 1988. "Dividend yields and expected stock returns," Journal of Financial Economics, Elsevier, vol. 22(1), pages 3-25, October.
    33. Stambaugh, Robert F., 1999. "Predictive regressions," Journal of Financial Economics, Elsevier, vol. 54(3), pages 375-421, December.
    34. Anat R. Admati, Paul Pfleiderer, 1988. "A Theory of Intraday Patterns: Volume and Price Variability," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 3-40.
    35. Alok Bhargava, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(3), pages 369-384.
    36. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    37. John Y. Campbell & Luis M. Viceira, 1999. "Consumption and Portfolio Decisions when Expected Returns are Time Varying," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(2), pages 433-495.
    38. Bruce N. Lehmann, 1988. "Fads, Martingales, and Market Efficiency," NBER Working Papers 2533, National Bureau of Economic Research, Inc.
    39. Summers, Lawrence H, 1986. "Does the Stock Market Rationally Reflect Fundamental Values?," Journal of Finance, American Finance Association, vol. 41(3), pages 591-601, July.
    40. DeGennaro, Ramon P. & Shrieves, Ronald E., 1997. "Public information releases, private information arrival and volatility in the foreign exchange market," Journal of Empirical Finance, Elsevier, vol. 4(4), pages 295-315, December.
    41. Peter M Robinson, 2001. "The Memory of Stochastic Volatility Models," STICERD - Econometrics Paper Series 410, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    42. 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.
    43. Bruce N. Lehmann, 1990. "Fads, Martingales, and Market Efficiency," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 105(1), pages 1-28.
    44. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
    45. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-227, June.
    46. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
    47. Henry L. Gray & Nien‐Fan Zhang & Wayne A. Woodward, 1989. "On Generalized Fractional Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(3), pages 233-257, May.
    48. Ooms, M., 1995. "Flexible Seasonal Long Memory and Economic Time Series," Econometric Institute Research Papers EI 9515-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    49. 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.
    50. John T. Barkoulas & Christopher F. Baum & Nickolaos Travlos, 1996. "Long Memory in the Greek Stock Market," Boston College Working Papers in Economics 356., Boston College Department of Economics.
    51. Cheung, Yin-Wong & Lai, Kon S., 1995. "A search for long memory in international stock market returns," Journal of International Money and Finance, Elsevier, vol. 14(4), pages 597-615, August.
    52. Gibbons, Michael R & Hess, Patrick, 1981. "Day of the Week Effects and Asset Returns," The Journal of Business, University of Chicago Press, vol. 54(4), pages 579-596, October.
    53. Robinson, P. M., 2001. "The memory of stochastic volatility models," Journal of Econometrics, Elsevier, vol. 101(2), pages 195-218, April.
    54. Robinson, Peter M., 2001. "The memory of stochastic volatility models," LSE Research Online Documents on Economics 2298, London School of Economics and Political Science, LSE Library.
    55. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
    56. Gil-Alana, Luis A., 1999. "Testing fractional integration with monthly data," Economic Modelling, Elsevier, vol. 16(4), pages 613-629, December.
    57. 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.
    58. Jegadeesh, Narasimhan & Titman, Sheridan, 1993. "Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," Journal of Finance, American Finance Association, vol. 48(1), pages 65-91, March.
    59. Robinson, Peter M. & Velasco, Carlos, 2000. "Whittle pseudo-maximum likelihood estimation for nonstationary time series," LSE Research Online Documents on Economics 2273, London School of Economics and Political Science, LSE Library.
    60. Peter M Robinson & Carlos Velasco, 2000. "Whittle Pseudo-Maximum Likelihood Estimation for Nonstationary Time Series - (Now published in Journal of the American Statistical Association, 95, (2000), pp.1229-1243.)," STICERD - Econometrics Paper Series 391, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    61. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    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. Cunado, Juncal & Gil-Alana, Luis A. & Gupta, Rangan, 2019. "Persistence in trends and cycles of gold and silver prices: Evidence from historical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 345-354.
    2. Guglielmo Maria Caporale & Luis Alberiko Gil‐Alana, 2022. "Trends and cycles in macro series: The case of US real GDP," Bulletin of Economic Research, Wiley Blackwell, vol. 74(1), pages 123-134, January.

    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. 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.
    2. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    3. Guglielmo Maria Caporale & Juncal Cuñado & Luis A. Gil-Alana, 2013. "Modelling long-run trends and cycles in financial time series data," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 405-421, May.
    4. Guglielmo Maria Caporale & Luis Gil-Alana, 2011. "The weekly structure of US stock prices," Applied Financial Economics, Taylor & Francis Journals, vol. 21(23), pages 1757-1764.
    5. Stéphane Goutte & David Guerreiro & Bilel Sanhaji & Sophie Saglio & Julien Chevallier, 2019. "International Financial Markets," Post-Print halshs-02183053, HAL.
    6. L.A. Gil-Alanaa, 2007. "Testing The Existence of Multiple Cycles in Financial and Economic Time Series," Annals of Economics and Finance, Society for AEF, vol. 8(1), pages 1-20, May.
    7. Committee, Nobel Prize, 2013. "Understanding Asset Prices," Nobel Prize in Economics documents 2013-1, Nobel Prize Committee.
    8. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    9. repec:ebl:ecbull:v:3:y:2004:i:7:p:1-10 is not listed on IDEAS
    10. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    11. L.A. Gil-Alana, 2005. "Fractional Cyclical Structures & Business Cycles in the Specification of the US Real Output," European Research Studies Journal, European Research Studies Journal, vol. 0(1-2), pages 99-126.
    12. repec:uts:finphd:39 is not listed on IDEAS
    13. Fernando Rubio, 2005. "Eficiencia De Mercado, Administracion De Carteras De Fondos Y Behavioural Finance," Finance 0503028, University Library of Munich, Germany, revised 23 Jul 2005.
    14. Arteche, Josu, 2004. "Gaussian semiparametric estimation in long memory in stochastic volatility and signal plus noise models," Journal of Econometrics, Elsevier, vol. 119(1), pages 131-154, March.
    15. repec:uts:finphd:38 is not listed on IDEAS
    16. Juncal Cunado & Luis A. Gil-Alana & Fernando Pérez de Gracia, 2002. "Is the US Fiscal Deficit Sustainable? A Fractionally Integrated and Cointegrated Approach," Faculty Working Papers 02/02, School of Economics and Business Administration, University of Navarra.
    17. 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.
    18. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    19. Zongwu Cai & Yongmiao Hong, 2013. "Some Recent Developments in Nonparametric Finance," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    20. Gil-Alana, Luis A., 2008. "A simple non-linear model with fractional integration for financial time series data," International Review of Financial Analysis, Elsevier, vol. 17(5), pages 838-848, December.
    21. Christensen, Bent Jesper & Nielsen, Morten Ørregaard & Zhu, Jie, 2010. "Long memory in stock market volatility and the volatility-in-mean effect: The FIEGARCH-M Model," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 460-470, June.
    22. Mark E. Wohar & David E. Rapach, 2005. "Return Predictability and the Implied Intertemporal Hedging Demands for Stocks and Bonds: International Evidence," Computing in Economics and Finance 2005 329, Society for Computational Economics.

    More about this item

    Keywords

    Stock market; Unit root cycles; Nonstationarity;
    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
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

    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:una:unccee:wp1503. 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: the person in charge (email available below). General contact details of provider: http://www.unav.edu/web/facultad-de-ciencias-economicas-y-empresariales .

    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.