Unit Root Tests with Wavelets
Simon Fraser University
Vanderbilt University - College of Arts and Science - Department of Economics
May 1, 2008
Econometric Theory, Vol. 26, pp. 1305-1331, 2010
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.
Number of Pages in PDF File: 30
Keywords: Unit root tests, cointegration, discrete wavelet transformation, maximum overlap wavelet transformation, energy decomposition
JEL Classification: C1, C2, C12, C22, F31, G0, G1Accepted Paper Series
Date posted: May 26, 2008 ; Last revised: December 24, 2011
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