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A test for the existence of a fractional root in a non-stationary time series

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  • Diego Lemus
  • Elkin Castaño

Abstract

In this work, we present a modification of the hypothesis testing procedure for the existence of long memory in the stationary and invertible ARFIMA(p,d,q) process proposed by Castaño, Gómez and Gallón (2008). This modification allows assessing the existence of a fractional root in a non-stationary time series when the short-term ARMA component is undetermined or unknown, especially in ARFIMA(p,d,q) processes. We validate, via Monte Carlo simulations, the analytical results and demonstrate the good performance of the proposed test in terms of both power and size, in comparison to other well-known tests in the literature.

Suggested Citation

  • Diego Lemus & Elkin Castaño, 2013. "A test for the existence of a fractional root in a non-stationary time series," Lecturas de Economía, Universidad de Antioquia, Departamento de Economía, issue 78, pages 151-184.
    • Handle: RePEc:lde:journl:y:2013:i:78:p:151-184
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    File URL: https://revistas.udea.edu.co/index.php/lecturasdeeconomia/issue/view/1336
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    More about this item

    Keywords

    Long memory time series; fractional differencing parameter; autoregressive approximation; nonstationary ARFIMA process;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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