Standard notation

Let’s establish a few basic notations to help us understand these strategies. We have a time series, Y_T, of T timesteps, y₁, …, y_T. Y_T denotes the same series but ending at timestep t. We also consider a function, W, which generates a window of size k > 0 from a time series.

This function is a proxy for how we prepare the input for the different models we have seen throughout the book. So if we see W(Y_t), it means the function will draw a window from Y_T that ends at timestep t. We will also consider H to be the forecast horizon, where H > 1. We will also use ; as an operator, which denotes concatenation.

Now, let’s look at the different strategies (Reference 1 is a good survey paper for different strategies). The discussion about merits and where we can use each of them is bundled in another upcoming section.