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Sorry for the newbie inquiry but I'm having a little trouble making sense of stationarity and how a the presence of a time trend impacts this. I'm working on a model for operating margins and as a first step I want to determine if the original series is stationary before proceeding. I first fitted a simple linear trend line to the data and the time regressor, while small in magnitude, registered as highly significant. I was always under the impression that this implied a non constant mean, thus non-stationary and may require a transform or differencing. I decided to regress the first differenced time series on the lag of the original time series and found the regressor of the lagged value to be negative and highly significant (t-stat greater than 9). This is where I got a little confused as these two seem to contradict my understanding of the subject. I thought a rejection of the null: g =0 (Dickey Fuller test) indicated no unit root, thus mean reverting and stationary. This seems to conflict with my initial assessment based on the deterministic time trend component. Thanks in advance!

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Every time series with a trend component is necessarily a non-stationary series. Non-trended series may or may not be stationary.

First plot your time series (if required logged series) to visualize the presence of trend. If there is an intuition for presence of trend, it means the series is not mean reverting, hence non-stationary.

To test for stationarity statistically, you can apply unit-root test.

For unit root test ADF method is most common as generally, there is auto-correlation in the series. If there is auto-correlation as well as heteroskedasticity in the series, select phillip perron method.

Use intercept or intercept + trend or none option as suggested by plot. If null hypothesis is rejected means series has no unit root, so it is stationary.

If not, use difference or transformation to make it stationary.

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