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Unit Root Tests with Wavelets

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  • Gencay, Ramazan
  • Fan, Yanqin

Abstract

This paper develops a wavelet (spectral) approach to test the presence of a unit root in a stochastic process. The wavelet approach is appealing, since it is based directly on the different behavior of the spectra of a unit root process and that of a short memory stationary process. By decomposing the variance (energy) of the underlying process into the variance of its low frequency components and that of its high frequency components via the discrete wavelet transformation (DWT), we design unit root tests against near unit root alternatives. Since DWT is an energy preserving transformation and able to disbalance energy across high and low frequency components of a series, it is possible to isolate the most persistent component of a series in a small number of scaling coefficients. We demonstrate the size and power properties of our tests through Monte Carlo simulations.

Suggested Citation

  • Gencay, Ramazan & Fan, Yanqin, 2007. "Unit Root Tests with Wavelets," MPRA Paper 9832, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:9832
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Unit root tests; discrete wavelet transformation; maximum overlap wavelet transformation; energy decomposition;

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics

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