I'm confused about the concept of stationarity. Most definitions require the mean and Variance to be constant 'over any interval'. This statement confuses me, if any interval should have the same mean mean and variance then I'll select a time-strip as narrow as possible, say 1 day where the graph is on a high and then another 1 day where the graph is on a low, then the mean is obviously different.
Say I take means over the green and blue bounds, they are going to be different, how is this a stationary time series then ? Moreover if trends and seasonality are not to be there in stationary time series data then what do models that require stationary data predict from, trends and seasonality are 'patterns' in the data, if they are not there than what is the basis of prediction, in that case how is stationary time series data of any use ?