I have a time series data, see jpg. It goes straight up and then straight down, later tailing off. This seems to fit my textbook’s description of a deterministic trend being an almost exact function of time on the way up and on the way down.
Using the D-F test I found that I could reject the existence of a unit root at the 5% level but not at the 1% level, and if I split the series into two parts, up and down, I cannot reject the unit root at even the 10% level.
Is it valid to use this time series, as it is (ie not differenced), in an OLS regression on the basis that it is a deterministic trend and therefore ‘trend stationary’? I want to run it as an explanatory variable against another series which is difference stationary.
When I did it, I found the answer to be reasonable (ie something similar to what I was expecting), the residuals did not show autocorrelation in a D-W test and I can reject a unit root in a D-F test at the 1% level.
Best Answer
Your series would appear to have a number of trends and possibly some asymptotic ARIMA structure. You can incorporate this series "as is" in a regression model. Detecting and identifying any needed lag structure using this variable would probably need suitable differencing.
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