# Trend Stationarity

1. May 14, 2012

### womata

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. May 14, 2012

### viraltux

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.

3. May 14, 2012

### womata

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?

4. May 14, 2012

### viraltux

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.

5. May 14, 2012

### womata

Thank you.

6. May 15, 2012

### viraltux

You're welcome