Testing Trend Stationarity in Time Series

  • Thread starter womata
  • Start date
In summary, the ADF test found that the series is non-stationary in level even when including a time trend. However, because the series is co-integrated of order zero, it is still valid to proceed with using cointegration methods.
  • #1
womata
6
0
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.
 
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  • #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.
 
  • #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?
 
  • #4
womata said:
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?

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
Thank you.
 
  • #6
You're welcome :smile:
 

1. What is the purpose of testing trend stationarity in time series?

The purpose of testing trend stationarity in time series is to determine whether a time series data set exhibits a stable, consistent trend over time. This is important in order to make accurate predictions and forecasts based on the data.

2. How is trend stationarity tested in time series?

Trend stationarity is typically tested using statistical tests such as the Augmented Dickey-Fuller (ADF) test or the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test. These tests analyze the data for the presence of a unit root, which indicates a non-stationary trend.

3. What does it mean if a time series is found to be non-stationary?

If a time series is found to be non-stationary, it means that the data does not exhibit a stable trend over time and is instead influenced by external factors. This can make it difficult to make accurate predictions and may require further analysis or adjustments to the data.

4. Are there any limitations to testing trend stationarity in time series?

Yes, there are some limitations to testing trend stationarity in time series. These tests assume certain conditions, such as a large number of observations and a linear trend. If these conditions are not met, the results of the test may be unreliable.

5. Can trend stationarity change over time?

Yes, trend stationarity can change over time. A time series that is initially found to be stationary may become non-stationary due to external factors or changes in the underlying data. It is important to regularly re-evaluate trend stationarity in order to make accurate predictions and forecasts.

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