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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
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    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. 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.
    3. L. A. Gil‐Alana, 2001. "Testing Stochastic Cycles in Macroeconomic Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(4), pages 411-430, July.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

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    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

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