- First, I performed ADF Test for unit root on a time series but series was not stationary.
- Therefore, I took first difference of series and then applied ADF test but now series become stationary but there is trend.
- Kindly suggest how to remove this trend using eviews.
I think you have some confusion about the meaning of stationarity. However, if still the test reports you have nonstationary data after using the first difference, you can use the second difference for the data. Also, you can use different tests, i.e. ADF and KPSS, for the same purpose.
First run Y on a constant and Time; collect the residuals (ee)
Then create Dee=ee-ee(-1);
Run Dee on ee(-1) Dee{1-8} -- -- I use 8 lags but you have to experiment here. I know you understand this step (see Perron lag criteria)..
Look at the t-value on ee(-1) to make your decision. I will be glad to explain further
Some Comments/Queries
1) You have used a constant and trend in your ADF tests of the level of the variable. If this is correct you should only use a constant in the test of the first difference.
2) Have you plotted the data? I would need to be convinced that there is a deterministic trend in crude oil prices.
3) It is not obvious that you are analyzing the log of the oil price. You should.
4) You should also be using the DF-GLS version of the unit root test as this is more powerful.
5. Consider using Structural Time Series Analysis (Kalman Filtering and Smoothing)
6. Alternatively look at the Hodrick-Prescott filter or the band pass filter of Christiano and Fitzgerald.
I have not used Eviews for many years but I would think that 4, 5 and 6 are implemented there
I think the suggestion by Professor Chuck makes sense. It seems you removed stochastic trend by differencing but not the deterministic trend. Detrending procedure is used when a trend is deterministic which I described below.
If Y_t is the trend-stationary process which is given as
Y_t = \alpha + \beta_t * trend + u_t, where trend = 1,2,..,T.
This process is known as deterministic non-stationarity and what is required is detrending. If we subtract the mean of Y_t from Y_t , the resulting series will be stationary, therefore the name trend-stationary. This way of removing the (deterministic) trend is called detrending.
i agree with the comments of Chuck A Arize and Akram Shavkatovich Hasanov
I agree with professor John C Frain.
I just want to add that, have in mind that the correct specification (regarding the deterministic components) in the ADF test plays a major role in the results. So you should plot the series first, and combining the graph with the some theory behind your variable's behavior (e.g. is it expected for this variable to have a deterministic trend or not? / what the graph seems like?) to decide about the deterministic parts you should use.
Also, bear in mind that the alternative hypothesis of the ADF test including both cosntant and trend is slightly different from the other cases. The rejection of the Null hypothesis under this specification indicates that the series is trend stationary (and not pure stationary as the otehr cases).
This means that is stationary after detrending (referring to deterministic trend).
Keeping all I said earlier the printouts are unusuaL The author includes no lags probably because DW is around 2.0, however, for one to rely on that the model must include a constan. The second point there is not enough lags in the equation so the claim for trend being significant is questionabl. Hansen‘s Lc is within the unit root part in E-views and could have been used for stabilit. Plots are okay for window dressing
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