Repeat the test with trend; trend and intercept for both Adf and pp.can apply Kpss  test and see.

thanks DR. Mousumi for your efforts

I think I solved the problem with 2nd difference

First, you have a small sample size but I will simply but a constant and trend with just enough lag to handle serial correlation. Second, plotting your data will give you an idea concerning the mean and the variance to see whether they are stationary or non-stationary. It doesn't make sense to use 10 lags, that is, definitely unacceptable given your sample size whether Ljung-Box or Box Pierce estimator. 

Dear my friend,

Firsly, you can check different modes of unit root test,i.e. with trend, without trend,..

Secondly, you can run other unit root tests to find out a better result.

Yours.

As Chuck has said 24 observations is small for an analysis of this size. Unit root tests will have size distortions and low power.  I do not know the nature of your variables but I would hope that they are at least annual. Can you make economic sense of your results. Some more details might enable a better answer

HI JOHN FRAIN

thanks for your efforts

Iam working on granger  casualty between FDI flow and GDP in annual bases Series ,data for unit root was tested in this regard , it's better to use 50 observations instead of 24  , but with regret  that's all  available data I obtained for FDI, at the same time for the first 10 years  series values were very low for example 322 million and it jumped after a decade  to 12097 million . I tried to use log GDP, results were the same. Anyhow, please find attachment for unit root test. I think 2nd difference will work out hopefully

HI EHSAN

thanks

I have done all three models you listed above , but  not sure whether to  convert my data to 2nd difference is the proper  things to do for this critical data.

re GDP : Changes in GDP are multiplicative i.e GDP tends to grow by some percent each year. You transform this to a linear additive model by using a log transform. Are you using nominal or real GDP? If you are using nominal your series is effected by both inflation and GDP growth. I would be inclined to think that the log of nominal GDP should be I(1).

re FDI: I presume that this is a nominal series. If FDI inflation and GDP inflation were linked this might lead to a spurious conclusion that FDI caused GDP.  Can you check if the early FDI data were in any way compatible with the later data. Were the earlier data netted in some way?  I suspect that your 10th significant lag is almost certainly due to the 10 years of earlier data being smaller than the next 10 years. Perhaps you can model the break in the series. At least you should have an explanation. There are proceedures for unit root tests in the persence of a break. (You should find Part IV of Maddala and Kim (1998), Unit Roots, Cointegration and Structural Change, Cambridge University Press useful )

If you can get over these problems I would suspect that log real GDP is I(1) and that log real FDI may also be I(1) but I would not expect them to be cointegrated. I would consider doing an analysis with their first differences augmented by some other variables.

In small samples theory and an understanding of the history of what you are analysing is very important.

Dear Dr. John C Frain

Many thanks for these valuable informations , this will direct me to do the correct analysis and true results.

Hello, 

Checking the stationary goes throw several steps, with trend and without, also with intercept or no, and you can check the optimal chosen lag by the AIC test. After that you check the stationary at level then at first different , and second different.

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Dear Jaafar,

Please check the optimal lag selection through AIC, SC or HQ. Then check your variables with the natural logarithmic form. Finally, check whether you should use trend and intercept.

Hope your problem  will be solved easily.

Yours!

When ADF and PP tests indicate mix results, you can apply KPSS test to affirm your results.. It is a stationarity test and it is known as an affirmative test..

One should not use the basic ADF or PP tests to test for unit roots. The PP test is poor in the size of sample available in econometric analysis. In particular the basic ADF is particularly poor when there is and MA element in the disturbance in the ADF regression. The DF-GLS test is a better version of an ADF type test.  This test is available in many econometric packages.  This is not covered or sometimes just mentioned  in many introductory texts. Maddala and Kim (1998) contains a good account of the efficacy of various unit root tests.

The treatment in most introductory texts uses the ADF and PP tests to explain and motivate testing for unit roots.

The KPSS test is a test with a null of stationarity. Using this in conjunction with a unit root test is not good practice. The purpose of a  unit root test is to "check" the compatibility of your data with an economic theory or model which implies a unit root. If your model implies stationarity a KPSS test can be used to "check" the compatibility of your data with stationarity. 

John is correct, although the common practice is to use the ADF and apply kpss whose null hypothesis stationarity as a cross-check. In all these cases, one should be careful because the alpha of 0.05 level is no longer correct.

Econometrics is the application of mathematical statistics to economic or financial data, therefore, stat and econometrics are very similar. Very often, applied statistics is econometrics when the data are Econ or financial. While a distinction exists, the difference is not much. The guy's question deals with unit root and I do not think a statistical answer will yield  a different conclusion

I would say that the rigor required for publication in a journal such as econometrica is equal to the requirements of any statistical journal and exceeds all but the best of them. Applied econometrics involving unit root tests is a mixture of economic and statistical theory applied to observational data and is intended to explain/expand/quantify some aspects of economics and is therefore more suitable for economic journals. Some early work on unit root theory was published in statistical journals.  Most of the theoretical work was done in econometric journals.

Chuck is 100% correct when he says that there is little distinction in statistical requirements when choosing between an econometric and a statistical journal. Choose a statistical journal when you are dealing with theory. Use an economic journal  when policy or economics is your aim.

Excellent explanation by Johnl. Much more effective and clarity than mine!

 Thanks for all participants and special thanks to john and chuck for intensive and rapid replies. It was very fruitful discussions that enhance understanding critical time series with  a complex case.