The paper „Stationary and Non-stationary Time Series” presents in a theoretical approach, the concept of time series, its characteristics which are: variability, homogeneity, periodicity and interdependence of time series terms, from which result the methods of estimation and analysis of time series, specific for each component (trend, periodical component-cyclical or seasonal, random component). As time series terms have or havn’t an evolution in time, it is stationary and non-stationary. In the case of stationary time series in the paper are defined the white-noise processes and the autoregressive processes. Since most processes are non-stationary by transformations we obtain stationary time series and in the paper are presented the restrictions for which an autoregresive process of moving average ARMA (p, q) is stationary. In the paper are approached also non-stationary processes by deterministic type and by stochastic type as the way to achieve stationary which mean the trend estimation and its elimination from the initial time series.