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Trend Stationarity

  1. May 14, 2012 #1
    Hello,

    I have two sets of time series that I found to be I(1), so I went ahead with using cointegration methods to find a relation between the two variables.

    Now I'm questioning if the series is trend-stationary, which would mean I'd need a deterministic time trend in my cointegration. I have done the ADF test on the series and found that even when including a time trend there, I still find that the series is non-stationary in level and stationary in first difference.

    Does this mean my series is not trend-stationary and that my initial approach is still valid? If what I did is wrong, how does one test for trend-stationarity?

    Thank you.
     
  2. jcsd
  3. May 14, 2012 #2
    ADF and the large family of unit root tests check exactly for that, yet there are cases where trend-stationarity is obvious in a plot and yet the tests do not detect it.

    Finance time series are typically I(1) and co-integrated of order zero. So if your time series have anything to do with finance that's the most likely scenario.
     
  4. May 14, 2012 #3
    It is a series for energy demand. If the ADF test says it is non-stationary in level even if I include a trend, and that my series is I(1), is it valid to proceed without detrending since all the statistical tests don't show a time trend?
     
  5. May 14, 2012 #4
    Sometimes it is not easy to distinguish a trend stationary series from a difference stationary one, that is why it is always a good idea to think about what kind of time series you are dealing with, for example, in countries with cold winters there will be a higher demand in winter than summer since everyone will use energy to warm their houses, so you know that you have a trend here and you can safely ignore whatever the test say, that is, the higher demand in winter is not due to a random process.

    Similarly in the stock market it's difficult to justify a trend and, unless it is a very special time series, you are better off assuming the existence of unit roots.
     
  6. May 14, 2012 #5
    Thank you.
     
  7. May 15, 2012 #6
    You're welcome :smile:
     
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