Hello Amer, The conclusion from the those hypotheses is simply that the ts is not stationary one. You need to transform your ts to a stationary one in the next step. This can be done by suitably differencing the ts or applying an appropriate transformation such as the logarithmic transformation or alternatively you may need to detrend the ts by fitting a linear model to it. You can apply the Box-Jenkins approach and fit a suitable ARIMA (p,d,q) model to your ts only after transforming your it to a stationary series.

Try looking at fractional integration tests (GRETL has a two simple ones that are built-in), where the degree of integration may be between 0 and 1.

In a presentation at the London Stata User's Group a few years ago, Prof. Chris Baum noted that the power of the ADF test is approximately 30 %, In other words, the beta for such a test is approximately 70%. Without a strong signal/noise ratio, you can't say much without proper qualification. You might consider a covariate adjusted ADF test or an Elliott, Stock, Rothenberg test as an alternative. As for the KPSS test, it has generated contradictory results according to Maddala and Kim in Unit Roots, Cointegration, and Structural Change(1998), Cambridge Univ. Press, 126-127, and a better test than that should be used when testing for stationarity.

Dear Dr. Yaffee & Sephton

thank you for your answers. i know what to do now.

Dr. Yaffee, would you please suggest other test than KPSS to be used for stationarity testing?

Dear Amer,

The Elliott-Stock-Rothenberg dfgls test is one of the more powerful tests

for nonstationarity for an ordinary time series. If you have structural breaks

or panel data, other tests may be considered.

- Regards,

Bob Yaffee

Dear Robert,

thank you i will check this;

best regards;

Hi Amer, further to Bob's suggestion, with respect to the KPSS test, you might want to check out a paper by Hobijn, Franses and Ooms in 2004: Statistica Neerlandica 58(4), December 2004. It extends the KPSS test to the case of no deterministic components and they show how different variance estimators affect the behaviour of the tests. Replication files are at http://www.frbsf.org/economic-research/economists/bart-hobijn/

Cheers

Peter

have you run ADF-GLS test on your data? what about PACF function?