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Exponential Time Trends in a Fractional Integration Model

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  • Guglielmo Maria Caporale
  • Luis Alberiko Gil-Alana

Abstract

This paper introduces a new modelling approach that incorporates nonlinear, exponential deterministic terms into a fractional integration model. The proposed model is based on a specific version of Robinson’s (1994) tests and is more general that standard time series models, which only allow for linear trends. Montecarlo simulations show that it performs well in finite sample. Three empirical examples confirm that the suggested specification captures the properties of the data adequately.

Suggested Citation

  • Guglielmo Maria Caporale & Luis Alberiko Gil-Alana, 2023. "Exponential Time Trends in a Fractional Integration Model," CESifo Working Paper Series 10774, CESifo.
    • Handle: RePEc:ces:ceswps:_10774
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    References listed on IDEAS

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    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. 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.
    4. 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.
    5. 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.
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    More about this item

    Keywords

    exponential time trends; fractional integration; Montecarlo 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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