In finance observables such as prices, interest rates, currency rates, etc are usually described by random variables. Thus for a satisfactory treatment you need to obtain their probability distributions. For the empirical measurement of the relevant probability distribution it is always easier if your observations are iid (=independent identically distributed). Clearly, if there is a "drift" term in your data, e.g. the mean of the data grows linearly in time, say, the iid-property will be gone. Therefore it makes sense to test for stationarity via a Dickey-Fuller unit root test: this gives you the 2nd "i" in iid (=identically). Next you need to check the 1st "i" of iid, that is the "independence". This can be done by the BDS test (Brock, Dechert and Scheinkman), which essentially looks at possible autocorrelations within the time series. If there are none you're done.

Respected Sir,

    I express my sincere Thanks for having clarified my doubts on stationarity.

In addition to the clean explanation by Markus Kreer to apply stationarity tests and to test for serial correlation of a series for checking IID assumptions - the longterm relationships are usually tested through Cointegration tests and its variants. In which case testing stationarity (for that matter absence of it) does make sense for taking the data to test for long run relationships.

Respected Nader Sir,

                         Thank You for having added an explanation on Stationarity Test..

Thank You.

Hi there, the long run and sort decomposition and Price Discovery, has been studied in commodities, using futures and spot in the paper by Isabel Figuerola-Ferretti & Jesus Gonzalo, 2010, Journal of Econometrics. I suggest you have a look...best

Respected Loannis Sir,

              Thanks a lot for having suggested a reference paper. I gained more information on price discovery in that paper. Thank You, Once again.