Time series stationarity

A time series is considered stationary if its statistical properties such as mean, variance, autocorrelation, and so on, are constant over time. Stationarity is important because most forecasting models run on the assumption that the time series is stationary or can be rendered (approximately) stationary using transformations. The reason for this approach is that values in a stationary time series are much easier to predict—if its properties are constant, we can simply state that they will be in the future as they were in the past. Once we forecast future values based on stationary time series, we can then reverse the process and the transformations to compute the values that would match the original series.

Thus, the properties of a stationary time series do not depend on the time when the series is observed. Implicitly, this means that time series that present seasonality or trends are not stationary. In this context, again, we must be careful of the difference...