A type of stochastic process that has received a great deal of attention and scrutiny by time SERIES ANALYSTS is the so-called stationary stochastic process. Broadly speaking, a stochastic process is said to be stationary if its mean and variance are constant over time and the value of the covariance between the two time periods depends only on the distance or gap or lag between the two time periods and not the actual time at which the covariance is computed. In the time series literature, such a stochastic process is known as a weakly stationary, or covariance stationary, or second-order stationary, or wide sense, stochastic process. 

In short, if a time series is stationary, its mean, variance, and autocovariance (at various LAGS) remain the same no matter at what point we measure them; that is, they are time invariant. Such a time series will tend to return to its mean (called mean reversion) and fluctuations around this mean (measured by its variance) will have a broadly constant amplitude.7 If a time series is not stationary in the sense just defined, it is called a nonstationary time series (keep in mind we are talking only about weak stationarity). In other words, a nonstationary time series will have a time-varying mean or a time-varying variance or both.

Why are stationary time series so important? Because if a time series is nonstationary, we can study its behaviour only for the time period under consideration. Each set of time series data will therefore be for a particular episode. As a consequence, it is not possible to generalize it to other time periods. Therefore, for the PURPOSE of forecasting, such (nonstationary) time series may be of little practical value. 

There are various ways to study non-stationarity of time series data – Augmented Dicky Fuller (ADF) test one of those very popular test to determine the nature of stationarity.