Effects of incorrect detrending on the coherency between non-stationary time series processes

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We study the effect of detrending on the coherency between two time series processes. Many economic and financial time series variables include nonstationary components; however, we analyze the two most popular cases of stochastic and deterministic trends. We analyze the asymptotic behavior of coherency under incorrect detrending, which includes the cases of first-differencing the deterministic trend process and, conversely, the time trend removal of the unit root process. A simulation study is performed to investigate the finite sample performance of the sample coherency due to incorrect detrending. Our work is expected to draw attention to the possible distortion of coherency when the series are incorrectly detrended. Further, our results can extend to various specification of trends in aggregate time series variables.

Original languageEnglish
Pages (from-to)27-34
Number of pages8
JournalCommunications for Statistical Applications and Methods
Issue number1
StatePublished - 1 Jan 2019

Bibliographical note

Publisher Copyright:
© 2019 The Korean Statistical Society, and Korean International Statistical Society.


  • Coherency
  • Deterministic trends
  • Detrending
  • Stochastic trends


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