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Testing for spurious and cointegrated regressions: A wavelet approach

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  • Chee Kian Leong
  • Weihong Huang

Abstract

This paper proposes a wavelet-based approach to analyze spurious and cointegrated regressions in time series. The approach is based on the properties of the wavelet covariance and correlation in Monte Carlo studies of spurious and cointegrated regression. In the case of the spurious regression, the null hypotheses of zero wavelet covariance and correlation for these series across the scales fail to be rejected. Conversely, these null hypotheses across the scales are rejected for the cointegrated bivariate time series. These nonresidual-based tests are then applied to analyze if any relationship exists between the extraterrestrial phenomenon of sunspots and the earthly economic time series of oil prices. Conventional residual-based tests appear sensitive to the specification in both the cointegrating regression and the lag order in the augmented Dickey-Fuller tests on the residuals. In contrast, the wavelet tests, with their bootstrap t-statistics and confidence intervals, detect the spuriousness of this relationship.

Suggested Citation

  • Chee Kian Leong & Weihong Huang, 2010. "Testing for spurious and cointegrated regressions: A wavelet approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(2), pages 215-233.
    • Handle: RePEc:taf:japsta:v:37:y:2010:i:2:p:215-233
    DOI: 10.1080/02664760802638082
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    1. repec:zbw:bofrdp:2005_001 is not listed on IDEAS
    2. Ramsey, J.B., 2002. "Wavelets in Economics and Finance: Past and Future," Working Papers 02-02, C.V. Starr Center for Applied Economics, New York University.
    3. Crowley, Patrick M., 2005. "An intuitive guide to wavelets for economists," Bank of Finland Research Discussion Papers 1/2005, Bank of Finland.
    4. Ramsey James B., 2002. "Wavelets in Economics and Finance: Past and Future," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(3), pages 1-29, November.
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