Dear Murugan

See this :

http://www.maths.bris.ac.uk/~guy/Research/LSTS/TOS.html

Stationarity means your data have no trend whether upwards or downward.  If you ever heard about ARIMA (p,d,q) and Sarima (p,d,q,) (P,D,Q)t., you have to use ACF and PACF in determine your value that represent for (p = PACF, d = differencing, q= ACF). I prefer you to use Minitab for this method 

A time serie may have a non seasonal non stationarity and seasonal non stationarity.

In order to test the non seasonal one, you've got to use the ADF test and the KPSS, they are complementary, and to test the non seasonal non stationnarity there is a test called Hegy. The the ACF correlogram may also help to know if your times series are non stationary when the the ACF are slowly decreasing.

A stochastic process is stationary in the weak sense if constant in mean and variance and the autocorrelation depends only on the number of lag k, not on t.

To test to a realization (or a data series) of a time series is stationary is that ACF and PACF is used. You can see the merits in the articles:

Akaike, Hirotugu (1974), “A new look at the statistical

model identification”, IEEE Transactions on Automatic

Control 19 (6): 716–723.

Akaike, Hirotugu (1980), “Likelihood and the Bayes

procedure”, in Bernardo, J. M.; et al., Bayesian

Statistics, Valencia: University Press, pp. 143–166.

We use for ADF test for the GNU R-Cran or Gretl software.

Any other question write to [email protected].

Thank you so much for sharing your answer

The Gretl (GNU) software to determine the stationarity of a series of data in an easy way, using unit root tests ADF, ADF-GLS, KPSS, Levin-Lin-Chu and fractional integration

What is the purpose of using ACF and PACF in time series data analysis? 

Right by using ACF anf PACF you will discover stationarity of your data

Might be late, but I'll try to answer. For a time series to be stationary, the following three components of the time series at any given time interval should be constant. 

• Mean
• Variance
• Co-variance

For this to happen we have  to remove seasons and trend in the time series. After removal of those, we do multiple test  to be sure that we have stationary time series.

Unfortunately, there exists no single test (as far as I know) that will tell you whether a time series is stationary in both the aspects mentioned (trend and seasonality). Some tests like DF, ADF handles only the trend aspect of time series and test like GARCH handles the seasonality aspect of time series.

So, it is necessary to carry out multiple series of tests to be sure that the time series is stationary.