stationarity

[jasil]

hi everyone, I have a question for you and I'm sure someone can help. please.
I have a serie which line graph shows one peak at the beginning and seams to have a positive trend at the end, so in this case and for what i know, this serie might not be stationary.
also I saw its correlogram and the autocorrelation function seems to have long memory, so it would confirm my conclusion of non stationarity.
however, when I look at the D-F Augmented test it says that this serie is a stationary one with 1% of significance.
so, should I conclude that despite all the observations of the graph and the correlogram this serie is stationay because the test D-F says so?
i really don't know how to decide this. when I saw the resoults of the D-F test i got really confused and tried looking at the first difference of my serie. the resoults are similar and the D-F Augmented test shows that this serie is also stationary but with 5% of significance.
or maybe someone can help me with other criteria for stating stationarity, thanks a lot.

[Pantera]

Hi,
Interesting question - I think you should send a new mail to the forum and attach the graph so everyone can take a look at it. Is it yearly or seasonal data you are analyzing?

Torbj.

[jasil]

hi torbj, thanks for your interest I really appreciate any help you all can give me. in response to your last post I just attached a Word file trying to explain with more details my original question.
hope now you can help me with some criteria to see wheter my variable is stationary or not. thanks a lot.

[jasil]

Hi Pantera, thank you so much for attending my question. I tried to add the deterministic trend to the ADF test function by chossing the option "trend and intercept" is it right? is that what you suggested? so the output window shows now the option @trend.
however, the test says that this time the serie ln E is stationary BUT with 5% of significance. what should I conclude? I appreciate a lot any help you can give me.
Once again I had to attach the doc with the Eviews resoults as pictures, sorry.

[Pantera]

Hi Jasil,
You have choosen the right option by including a deterministic trend in the test function. It seems to me that the series could be a border case between having a unit not and not. However, by looking at the output you have attached, we cannot see whether the determinstic trend is significantly different from zero. If the determinstic trend is not significantly different from zero, than you can conclude (due to the large t-value on the y(t-1)-coefficient in the ADF-test function. On the other hand if you do a F-test of the hypothesis: coefficient y(t-1) and coefficient to the determinstic trend is simultanously zero, and the test shows that both coefficients are NOT different from zero, than run a modified ADF test where you do NOT include the deterministic trend. This is actually the test you first presented for us (June 25). Well, firstly - tell us first whether the trend is different from zero or not. Check also whether the residuals are autocorrelated (first and higher order) --by checking the automatic "resid".

Regards,
Pantera

[Pantera]

Hi - I forgot to mention that the critical values applied in the F-test I'm referring to is not identical (due to non-asymptotic properties) to the critical F-values applied in ordinary F-tests. See for example: Dickey and Fuller (1981): "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root". Econometrica 49, pp. 1057-72.

To sum up: You start with the ADF-test function which includes a determinstic trend - which you now have done. The output indicates a unit root. But you must also test the role of the determinstic trend. The referred F-test tests whether both coefficients (for the lagged dependent variable y(t-1) and the determinstic trend) are zero. If they are zero - you exclude the determinstic trend from the ADF-test function, and you are actually back to the results you presented June 25. According to these results you can conclude that series has no unit root. If the F-test results in a rejection of the null hypothesis, i.e. you reject that both coefficients are simultaneously zero, than you can also can conclude that the series has no unit because the t-value of the lagged y(t-1) is -3.69 (according to you output). In this case you can evaluate the coefficient by using the same critical t-values which you use when you evaluate coefficients in regression with stationary variables.


Regards,
Pantera

[jasil]

hi Pantera, first I want to thank you for responding my posts all your comments are really helpful, thanks a lot. The reason for my delay is that I've been looking for the Dickey and Fuller book you recommended, I'm really frustrated because I couldn't find it or any other reference to the F-test you were talking about.
I'm stucked cause have no clue of this test or any way to determine the hypotesis. I totally understood what you are suggesting me to do but I don't know how to determine whether both coefficients are zero. Can you still help me? do you want to? thanks a lot anyway.

[jasil]

hi Pantera, here you have the serie of the variable LnE that i'm testing in an Excel fila, sorry about that but it's the only way I could attach the document. i would've send you a message but the page doesn't allow me to add any doc. thanks a lot.