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UNIT ROOT TESTS WITH WAVELETS

  • Yanqin Fan (a1) and Ramazan Gençay (a2)
  • DOI: http://dx.doi.org/10.1017/S0266466609990594
  • Published online: 01 February 2010
Abstract

This paper develops a wavelet (spectral) approach to testing 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.

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Corresponding author
*Address correspondence to Ramazan Gençay, Department of Economics, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, V5A 1S6, Canada; e-mail: rgencay@sfu.ca.
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