Time series analysis: the effect of adding an unsupervised layer to NN time series prediction

Let {Yt} be an observed time series where the interval between observations is fixed. We consider models which take a window of length d of the time series so that Ys+d is the response to 〈Ys, Ys+1, . . . , Ys+d−1〉. We will train the models to predict the next observation in the time series. In order to predict an observation some number of periods f in the future we will predict the next observation and iterate the predictor. The method of stochastic sampling may be also used [1] but we will not consider it here.