Just to make sure I understand it correctly. So, stationary time series is where the mean and variance are slightly different or almost the same in each sliding window? And for non-stationary, it is mean that there will be a trend, seasonal or both together in that time series?
There’s nothing wrong in ignoring the stationary nature of the data and feeding it to the model. Laurence suggests training your model on the last few steps could yield better performance i.e. past the big event point since the last few data points more representational of future values (see this lecture) than the earlier ones.
Your understanding of stationary timeseries is correct. Given that trend and seasonality are the key factors behind making a stationary time series non-stationary, we can remove these components before building a model. Please look at the assignment for the week to get a better picture.