Unit Root Tests with Wavelets

30 Pages Posted: 26 May 2008 Last revised: 24 Dec 2011

See all articles by Ramazan Gencay

Ramazan Gencay

Simon Fraser University

Yanqin Fan

University of Washington - Department of Economics

Date Written: May 1, 2008


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.

Keywords: Unit root tests, cointegration, discrete wavelet transformation, maximum overlap wavelet transformation, energy decomposition

JEL Classification: C1, C2, C12, C22, F31, G0, G1

Suggested Citation

Gencay, Ramazan and Fan, Yanqin, Unit Root Tests with Wavelets (May 1, 2008). Econometric Theory, Vol. 26, pp. 1305-1331, 2010, Available at SSRN: https://ssrn.com/abstract=906975

Ramazan Gencay (Contact Author)

Simon Fraser University ( email )

Department of Economics
8888 University Drive
Burnaby, British Columbia V5A 1S6

Yanqin Fan

University of Washington - Department of Economics ( email )

Box 353330
Seattle, WA 98195-3330
United States

HOME PAGE: http://econ.washington.edu/people/yanquin-fan/

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