Stationary Time Series
The process of most time series models requires conditions that are stationary from the start before any autoregressive components, differencing, or averaging is performed.
First Order Stationary
A time series is first order stationary when underlying conditions exist, but there is no trend or seasonality in the data. In other words, the predictions for all time points t are based on these same underlying conditions.
Second Order Stationary
The series becomes second order stationary when the predicted forecast for any given point t has some kind of trend component added to the underlying conditions.