Testing for spurious and cointegrated regressions: A wavelet approach

Chee Kian Leong, Weihong Huang

Research output: Journal PublicationArticlepeer-review

4 Citations (Scopus)


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 failto berejected. 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.

Original languageEnglish
Pages (from-to)215-233
Number of pages19
JournalJournal of Applied Statistics
Issue number2
Publication statusPublished - Feb 2010
Externally publishedYes


  • Bootstrap
  • Cointegration
  • Monte Carlo simulations
  • Spurious regression
  • Wavelet covariance and correlation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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