The purpose of this article is to introduce the basic elements of what is considered to be the missing piece in the time series puzzle, cointegration. We begin by defining the spurious regression and the notion of nonstationary, the departure point for cointegrated series. We explain the meaningful core of cointegration, as equilibrium process, as well as the connection with the error correction model and with the Granger Representation Theorem. As the proof of the mentioned theorem offers a deeper understanding of the mechanisms lying behind the presented phenomena,, we decided to also provide a sketch of the proof. The article continues with procedures used to test for the existence of cointegration and to estimate the cointegration vectorial space. In order to support this, we will revise, as methodology and as well as logical deduction, the Engle Granger two stage procedure, mainly utilized in bivariate systems, and the Johansen procedure, utilized in multivariate systems. As an applicative study, we have chosen to set up a study on the stock market. The capital market having the stock exchange series evolving as Random Walk processes proves itself being an excellent candidate in testing the cointegrated systems. We have chosen three series of stock exchange indexes, from Romania, France and US, series with daily frequencies. Using unit root tests ,Dickey Fuller, we find that the three series are nonstationary, moreover each of the series is integrated of first order. Afterwards we test the existence of cointegration with the Engle Granger procedure. We find that the series BET and CAC40 are cointegrated, thus we can estimate an error correction model, and we find that about 2% of the distance between the two series is corrected daily, as we have daily observations. Eventually we run the Johanses procedure – the three series form a cointegrated system, the dimension of the cointeration space is one.