Abstract-enerally speaking, in research area attention is focused on the latest news and practitioners are trying to interpret them, and not at least to forecast their future patterns. Right along, the key feature of time series analysis is given by stationarity which represents the foundation of all the mathematical models developed in the recent past. This paper illustrates the importance of stationarity in time series analysis and the most used statistical tests for checking the stationarity of a series: Augmented Dickey -Fuller Test and Phillips-Perron Test, by making use of the most three important U.S. indices: Dow Jones Industrial Average Index (September 10, 1928 to September 26, 2016), S&P 500 Index (December 09, 1957 to September 26, 2016) and Russell 3000 Index (December 09, 1986 to September 26, 2016), daily quotations, which involves investigating three time series of 22216 observations, 14818 observation and 7513 observations. The analysis revealed non-stationarity in levels in case of all three indices and stationarity in first difference for all three analyzed time series. This came as no surprise since the Box-Jenkins approach for modeling time series stated that financial time series are non-stationary. Thereby, it is a fact that for building elaborate structures (in our case -elaborate models) the first step consists in building simple parts which arranged together in some way leads to complexity. Furthermore, that simple part which allows the existence of the complex structures is stationarity. Keywords-Stationarity, Augmented Dickey -Fuller Test, Phillips-Perron Test, Time Series Analysis, Dow JonesIndustrial Average Index, S&P 500 Index, Russell 3000 Index I. INTRODUCTION. LITERATURE REVIEWThe study and analysis of the economic phenomena is performed using time series. It is worth mentioning that the importance of stationarity of a time series is represented by stability, the feature required to make statements about the future, so to get valid forecasts. -Time series represents a source of information for analysis and economic forecast, and reveals knowledge items which are useful for research or economic activity.‖ ([12], pp. 23).Techniques for analyzing the dependence of the adjoining observations require -the development of stochastic and dynamic models for time series data and the use of such models in important areas of application‖ ([3], pp. 07). The Box-Jenkins approach for modeling time series stated that financial time series are non-stationary since the mean changes over time, so they proceeded to differentiate the data in order to obtain stationarity. On the other hand, the modern econometrics is based on the concept of cointegration and the cointegration analysis depends on the nonstationarity of time series, thus the first thing done is to investigate the time series for the presence of a unit root.Thereby, even if we talk about autoregressive integrated moving average processes, based on Box-Jenkins methodology, or other techniques like cointegration -seen as the dynamic link...

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