Deep Learning for Time Series Forecasting

So far in this book, we have described traditional statistical methods for time series analysis. In the preceding chapters, we has discussed several methods to forecast the series at a future point in time from observations taken in the past. One such method to make predictions is the auto-regressive (AR) model, which expresses the series at time t as a linear regression of previous p observations:

 

Here, Є_t is the residual error term from the AR model.

The idea underlying the linear model can be generalized that the objective of time series forecasting is to develop a function f that predicts x_t in terms of the observations at previous p points of time:

x_t = f(x_t-1,x_t-2, ... ,x_t-p)

In this chapter, we will explore three methods based on neural networks to develop the function f. Each method includes defining a neural network...