IDEAS home Printed from https://ideas.repec.org/a/gam/jecnmx/v12y2024i2p15-d1406442.html
   My bibliography  Save this article

Exponential Time Trends in a Fractional Integration Model

Author

Listed:
  • Guglielmo Maria Caporale

    (Department of Economics and Finance, Brunel University, London UB8 3PH, UK)

  • Luis Alberiko Gil-Alana

    (Faculty of Economics and ICS, University of Navarra, E-31080 Pamplona, Spain
    Universidad Francisco de Vitoria, Facultad de Ciencias Juridicas y Empresariales, Madrid, Spain)

Abstract

This paper introduces a new modelling approach that incorporates nonlinear, exponential deterministic terms into a fractional integration framework. The proposed model is based on a specific test on fractional integration that is more general than the standard methods, which allow for only linear trends.. Its limiting distribution is standard normal, and Monte Carlo simulations show that it performs well in finite samples. Three empirical examples confirm that the suggested specification captures the properties of the data adequately.

Suggested Citation

  • Guglielmo Maria Caporale & Luis Alberiko Gil-Alana, 2024. "Exponential Time Trends in a Fractional Integration Model," Econometrics, MDPI, vol. 12(2), pages 1-14, May.
    • Handle: RePEc:gam:jecnmx:v:12:y:2024:i:2:p:15-:d:1406442
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2225-1146/12/2/15/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2225-1146/12/2/15/
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Stock, James H & Watson, Mark W, 1988. "Variable Trends in Economic Time Series," Journal of Economic Perspectives, American Economic Association, vol. 2(3), pages 147-174, Summer.
    2. Tolga Omay & Rangan Gupta & Giovanni Bonaccolto, 2017. "The US real GNP is trend-stationary after all," Applied Economics Letters, Taylor & Francis Journals, vol. 24(8), pages 510-514, May.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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. F. DePenya & L. Gil-Alana, 2006. "Testing of nonstationary cycles in financial time series data," Review of Quantitative Finance and Accounting, Springer, vol. 27(1), pages 47-65, August.
    2. 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.
    3. 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.
    4. Cho, Cheol-Keun & Amsler, Christine & Schmidt, Peter, 2015. "A test of the null of integer integration against the alternative of fractional integration," Journal of Econometrics, Elsevier, vol. 187(1), pages 217-237.
    5. Axel Bücher & Holger Dette & Florian Heinrichs, 2023. "A portmanteau-type test for detecting serial correlation in locally stationary functional time series," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 255-278, July.
    6. Mohamed Chikhi & Anne Péguin-Feissolle & Michel Terraza, 2013. "SEMIFARMA-HYGARCH Modeling of Dow Jones Return Persistence," Computational Economics, Springer;Society for Computational Economics, vol. 41(2), pages 249-265, February.
    7. Luis A. Gil-Alana, 2004. "Structural Change and the Order of Integration in Univariate Time Series," Computational Economics, Springer;Society for Computational Economics, vol. 23(3), pages 239-254, April.
    8. Guneratne B Wickremasinghe & Jae H Kim, 2008. "Weak-Form Efficiency of Foreign Exchange Markets of Developing Economies," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 7(2), pages 169-196, August.
    9. 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.
    10. Podivinsky, Jan M. & King, Maxwell L., 2000. "The exact power envelope of tests for a unit root," Discussion Paper Series In Economics And Econometrics 0026, Economics Division, School of Social Sciences, University of Southampton.
    11. Uäžur Sivri, 2017. "Is Inflation Rate Of Turkey Stationary? Evidence From Unit Root Tests With And Without Structural Breaks," Review of Economic and Business Studies, Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, issue 20, pages 29-52, December.
    12. Tilak Abeysinghe & Gulasekaran Rajaguru, 2009. "A Gaussian Test for Cointegration," Microeconomics Working Papers 22013, East Asian Bureau of Economic Research.
    13. Rodrigues, Paulo M. M. & Taylor, A. M. Robert, 2004. "Alternative estimators and unit root tests for seasonal autoregressive processes," Journal of Econometrics, Elsevier, vol. 120(1), pages 35-73, May.
    14. Podivinsky, Jan M. & King, Maxwell L., 2000. "The exact power envelope of tests for a unit root," Discussion Paper Series In Economics And Econometrics 26, Economics Division, School of Social Sciences, University of Southampton.
    15. Luis A. Gil-Alana, 2004. "Testing of I(d) processes in the real output," Economics Bulletin, AccessEcon, vol. 3(32), pages 1-6.
    16. Karin Niehoff, 2016. "Price Discovery in Voting and Non-Voting Stocks," Schmalenbach Business Review, Springer;Schmalenbach-Gesellschaft, vol. 17(3), pages 285-307, December.
    17. Caporale, Guglielmo Maria & Gil-Alana, Luis Alberiko & Puertolas, Francisco, 2024. "Modelling profitability of private equity: A fractional integration approach," Research in International Business and Finance, Elsevier, vol. 67(PA).
    18. Hwang, Jaeyoun & Schmidt, Peter, 1996. "Alternative methods of detrending and the power of unit root tests," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 227-248.
    19. Cretí, Anna & Joëts, Marc, 2017. "Multiple bubbles in the European Union Emission Trading Scheme," Energy Policy, Elsevier, vol. 107(C), pages 119-130.
    20. Maria Malmierca-Ordoqui & Luis A. Gil-Alana & Lorenzo Bermejo, 2024. "Private and public debt convergence: a fractional cointegration approach," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 51(1), pages 161-183, February.

    More about this item

    Keywords

    exponential time trends; fractional integration; Monte Carlo simulations;
    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
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

    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:gam:jecnmx:v:12:y:2024:i:2:p:15-:d:1406442. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.