The statistical properties, such as the mean, variance, or autocorrelation, of a stationary time series are independent of the period, that is, they don't change over time. Hence, stationarity implies that a time series does not have a trend or seasonal effects and that descriptive statistics, such as the mean or the standard deviation, when computed for different rolling windows, are constant or do not change much over time. It reverts to its mean, and the deviations have constant amplitude, while short-term movements always look the same in the statistical sense.

More formally, strict stationarity requires the joint distribution of any subset of time series observations to be independent of time with respect to all moments. So, in addition to the mean and variance, higher moments such as skew and kurtosis, also need to be constant, irrespective of the lag between different observations. In most applications, we limit stationarity to first and second moments so that the time series is covariance stationary with constant mean, variance, and autocorrelation. 

Note that we specifically allow for dependence between observations at different lags, just like we want the input data for linear regression to be correlated with the outcome. Stationarity implies that these relationships are stable, which facilitates prediction as the model can focus on learning systematic patterns that take place within stable statistical properties. It is important because classical statistical models assume that the time series input data is stationary. 

The following sections introduce diagnostics that help detect when data is not stationary, and transformations that help meet these assumptions.