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Unit Root Tests With Wavelets

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  • Fan, Yanqin
  • Gençay, Ramazan

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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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 26 (2010)
Issue (Month): 05 (October)
Pages: 1305-1331

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Handle: RePEc:cup:etheor:v:26:y:2010:i:05:p:1305-1331_99

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  1. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, Econometric Society, vol. 58(1), pages 113-44, January.
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Cited by:
  1. Michis, Antonis A., 2014. "Time scale evaluation of economic forecasts," Economics Letters, Elsevier, vol. 123(3), pages 279-281.
  2. Javier Fernandez-Macho, 2013. "A wavelet approach to multiple cointegration testing," Economics Series Working Papers 668, University of Oxford, Department of Economics.
  3. Li, Linyuan & Yao, Shan & Duchesne, Pierre, 2014. "On wavelet-based testing for serial correlation of unknown form using Fan’s adaptive Neyman method," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 70(C), pages 308-327.
  4. Almasri, Abdullah & Månsson, Kristofer & Sjölander, Pär & Shukur, Ghazi, 2012. "Testing for Panel Unit Roots in the Presence of an Unknown Structural Break and Cross-Sectional Dependency," HUI Working Papers, HUI Research 63, HUI Research.
  5. Gallegati, Marco & Ramsey, James B., 2013. "Bond vs stock market's Q: Testing for stability across frequencies and over time," Journal of Empirical Finance, Elsevier, Elsevier, vol. 24(C), pages 138-150.
  6. Tiwari, Aviral Kumar & Dar, Arif Billah & Bhanja, Niyati, 2013. "Oil price and exchange rates: A wavelet based analysis for India," Economic Modelling, Elsevier, vol. 31(C), pages 414-422.
  7. Yushu Li & Ghazi Shukur, 2013. "Testing for Unit Roots in Panel Data Using a Wavelet Ratio Method," Computational Economics, Society for Computational Economics, Society for Computational Economics, vol. 41(1), pages 59-69, January.

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