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I would like to determine if there is any association between two time series. One of the time series is stationary, the other is not stationary. In this scenario does a cointegration test make sense and if so what R based test/package can I use? I have been using the Johansen procedure in R for scenarios where both time series are non-stationary.

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No, you cannot consider cointegration between a stationary and an integrated time series. A prerequisite for cointegration is that all of the series under consideration are integrated of order one or greater to begin with. For an introduction to cointegration you may refer to Lütkepohl "New introduction to multiple time series analysis" (2005) or any other modern (post 1990) time series textbook.

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