Unit root test ADF

[terran190]

Hi,

I have some practical questions that really need your help.

When I use the ADF, do I need to test the series for all 3 specifications or there is any way to decide the specification for the series?
And in case if I test for 3 specifications and 2 of the values of the test lead to rejection/no rejection, does that mean we can conclude base on the rule of majority?

Thanks a lot.

[bensamen]

Hey,

First, dont forget that plotting data and observing the graph is sometimes useful bcz it can clearly indicate the presence or not of deterministic regressors.

However, we practically proceed as follow when doing a ADF uroot test.

1. Estimate the most general model with trend and intercept. And then check the stationarity on the first part of the output. If the data is non-stationary (i.e. the computed absolute t-statistic is smaller than the absolute critical value or the prob is > 5% ), then you need to check on the second part of the output whether the trend coefficient (@trend) is significant or not.
- If the @trend is significant, you can conclude that you have data with deterministic trend. To have it stationary, you can use either Trend-Stationary Process (TSP) or Difference-Stationary Process (DSP).
- If the @trend isnot significant, then you have to estimate the model with intercept.
2. If the model with intercept is non-stationary, you can at least to check the constant term to be sure if you have a stochastic trend with constant or not.
3. Lastly, you can use the none model.
PS. 1. The data generate by a stochastic trend are stationary only by using Difference-Stationary Process (DSP).
2. After having a deterministic trend stationary using Trend-Stationary Process (TSP), you dont have to check its stationary with the full model (with intercept and trend).

Best regards,

[terran190]

Hi, thanks for your reply. I did follow your instructions, but still I have some more questions regarding this problem, hope you can help me:
- For step 1, if I check the model with trend and intercept and got a result of stationary, does it mean that I can conclude the series is stationary without checking the other 2? I think I also have to check the significance of @trend, if not significant then it is not the true model, hv to check the other 2.
- If the time series is not stationary and @trend is significant, you said that I just have to difference it to make the series stationary, does that mean I just difference it once, or I also have to check the t-stat of both the 1st level and 2nd level to make sure which one is correct?
- And if I conclude that the time series is with determistic trend and nonstationary, then for testing the unit root for 1st level and 2nd level, I just have to test for determistic trend or I have to do all 3 models?

I know that these questions may look stupid, but I am so confused and cannot think it straight now...

Thanks for your help

[terran190]

I figured out some number of steps already, but still 1 more question: If you know that the series is nonstationary, how to conclude that it is I(1) or I(2)? Using the option 1st difference and 2nd difference like we did with level option?

[bensamen]

First of all, there's no stupid questions here since it is a forum when we can discuss and help each other up.

If you know that the series is nonstationary, how to conclude that it is I(1) or I(2)? Using the option 1st difference and 2nd difference like we did with level option?

Yeah. I(1) means that you used first difference to have your raw data stationary and I(2) means 2st difference as well.

- For step 1, if I check the model with trend and intercept and got a result of stationary, does it mean that I can conclude the series is stationary without checking the other 2? I think I also have to check the significance of @trend, if not significant then it is not the true model, hv to check the other 2.

I think that when your conclude that the full model is stationary, we dont have to check the trend again, the 2 other models either.

- If the time series is not stationary and @trend is significant, you said that I just have to difference it to make the series stationary, does that mean I just difference it once, or I also have to check the t-stat of both the 1st level and 2nd level to make sure which one is correct?

First, you difference once and begin the process from the second model (with intercept) because the trend effect is generally eliminated during the first difference. But you can definitively check the full model so far.

[terran190]

Thanks buddy, I figured that out alr :D
Can you take a look at my question about the causality test also if you dont mind :)

Code: Select all

I have some questions relating the causality test. After I did the Engle-Granger cointegration part, I found that most of them are co-integrated. As far as I know, the standard Granger-causality test is invalid and a more comprehensive test of causality based on ECM, am I right? If that is the case, I want to ask how can I estimate an ECM in Eviews? And then I have to perform a causality test via "view - lag structure - granger causality/block exogeneity test?

[xnder]

"Pfaff, Analysis of Integrated and Cointegrated time series (with R) - 2008"
can help you on this topic. There is a great testing framework about ADF testing procedure.

[j52]

Your discussion was quite helpful. I still have one question..

assuming the level data is nonstationary and testing the first difference I get for
- trend and intercept --> non-stationary and insignificant trend
- intercept --> stationary (c insignificant)

thus I have a stochastic trend. Do I need to use the first or second difference to analyse the series?

[ecomary]

Hello
I read the dear bensamen's explanation. But I have a primary question from the first of explanation: How can I examin the @trand? Where can I find absolut critical valu of t-student to examin @trand? Can I examin it by its prob that is infront of it?
And another question: in the books have wroten that unit root test ADF have 10 steps, have you ever seen it? I can't do these 10 steps by EViews but I can do what "bensamen" said for unit root test, are these tow way diferent or not? Can I do bensamen's explenation instead of those 10 steps?
Pleas help me. Thank you very much
Best regards

[ecomary]

pleas one person reply me. I realy need your reply.

[Emm jay]

please any one can help me,, i hv some problems and confusion about ADF test..
when i apply unit root at my variable say BD,, it got stationary at 2nd difference with automatic lag selection which is 7,, and with my selection 3 also .. as it got stationary but didn't give satisfactory results because trend and intercept both are insignificant and D.W value is also high. but if i put zero lag length it got stationary at 1st difference plus trend and DW is also significant...
so please tell me would it be appropriate to set lag length equal zero?

[tajuddinaznan]

Hi Everyone,

I would like to seek some help as I need to replicate data in the article but I couldnt understand some of the article statement "We employ the Augmented Dickey-Fuller test (1979)for this purpose. Table 1 displays the results of the Augmented Dickey-Fuller tests. In each case, a log polynomial in first differences of each variable was taken out six periods to render the residuals approximate white noise. We used monthly data from 1965-2005 to empirically analyze the relationship between money supply and stock prices."

I have tried using the ADF from Eviews but the result is not the same. I think it is bcoz the bolded statement above which i think need some adjustment.

What does the author mean of the "log polynomial in first differences of each variable was taken out six periods to render the residuals approximate white noise"? How can I make this adjustment using Eviews?

Thanks