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A wavelet approach to multiple cointegration testing

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  • Javier Fernandez-Macho

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.

Suggested Citation

  • Javier Fernandez-Macho, 2013. "A wavelet approach to multiple cointegration testing," Economics Series Working Papers 668, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:668
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    File URL: http://www.economics.ox.ac.uk/materials/papers/12782/paper668.pdf
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    References listed on IDEAS

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    1. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    2. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Oxford University Press, vol. 53(4), pages 473-495.
    3. Christoph Schleicher, 2002. "An Introduction to Wavelets for Economists," Staff Working Papers 02-3, Bank of Canada.
    4. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    5. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 99-125.
    6. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "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?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    7. Patrick M. Crowley, 2007. "A Guide To Wavelets For Economists ," Journal of Economic Surveys, Wiley Blackwell, vol. 21(2), pages 207-267, April.
    8. Daniel Levy, 2002. "Cointegration in Frequency Domain," Emory Economics 0209, Department of Economics, Emory University (Atlanta).
    9. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    10. Haug, Alfred A., 1996. "Tests for cointegration a Monte Carlo comparison," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 89-115.
    11. 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.
    12. Fan, Yanqin & Gençay, Ramazan, 2010. "Unit Root Tests With Wavelets," Econometric Theory, Cambridge University Press, vol. 26(05), pages 1305-1331, October.
    13. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-1056, September.
    14. Shin, Yongcheol, 1994. "A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration," Econometric Theory, Cambridge University Press, vol. 10(01), pages 91-115, March.
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    More about this item

    Keywords

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

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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