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A wavelet approach to multiple cointegration testing

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  • Javier Fernandez-Macho
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    Abstract

    This paper introduces a class of cointegration tests based on estimated low-pass and high-pass regression coefficients from the same wavelet transform of the original time series data.� The procedure can be applied to test the null of cointegration in a n + k multivariate system with n cointegrating relationships without the need of either detrending nor differencing.� The proposed non residual-based wavelet statistics are asymptotically distributed as standard chi-square with nk degrees of freedom regardless of deterministic terms or dynamic regressors, thus offering a simple way of testing for cointegration under the null without the need of special tables.� Small sample quantiles for these wavelet statistics are obtained using Monte Carlo simulation in different situations including I(1) and higher order cointegration cases and it is shown that these wavelet tests exhibit appropriate size and good power when compared to other tests of the null of cointegration.

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    Bibliographic Info

    Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 668.

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    Date of creation: 11 Jul 2013
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    Handle: RePEc:oxf:wpaper:668

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    Related research

    Keywords: Brownian motion; cointegration; econometric methods; integrated process; multivariate analysis; spectral analysis; time series models; unit roots; wavelet analysis;

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    1. Daniel Levy, 2002. "Cointegration in Frequency Domain," Emory Economics, Department of Economics, Emory University (Atlanta) 0209, Department of Economics, Emory University (Atlanta).
    2. Christoph Schleicher, 2002. "An Introduction to Wavelets for Economists," Working Papers, Bank of Canada 02-3, Bank of Canada.
    3. Haug, Alfred A., 1996. "Tests for cointegration a Monte Carlo comparison," Journal of Econometrics, Elsevier, Elsevier, vol. 71(1-2), pages 89-115.
    4. Fan, Yanqin & Gençay, Ramazan, 2010. "Unit Root Tests With Wavelets," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 26(05), pages 1305-1331, October.
    5. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, Econometric Society, vol. 55(5), pages 1035-56, September.
    6. Peter C.B. Phillips & Steven N. Durlauf, 1985. "Multiple Time Series Regression with Integrated Processes," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 768, Cowles Foundation for Research in Economics, Yale University.
    7. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 979, Cowles Foundation for Research in Economics, Yale University.
    8. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 283-306, March.
    9. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 57(1), pages 99-125, January.
    10. Leybourne, S J & McCabe, B P M, 1994. "A Simple Test for Cointegration," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 56(1), pages 97-103, February.
    11. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
    12. Patrick M. Crowley, 2007. "A Guide To Wavelets For Economists ," Journal of Economic Surveys, Wiley Blackwell, Wiley Blackwell, vol. 21(2), pages 207-267, 04.
    13. Shin, Yongcheol, 1994. "A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 10(01), pages 91-115, March.
    14. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, Econometric Society, vol. 55(2), pages 251-76, March.
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