Time delay embedding

The basic idea behind time delay embedding is to embed time in terms of recent observations. If you want to head back to Chapter 5, Time Series Forecasting as Regression, and review this concept (Figure 5.1), please go ahead and do so now.

In Figure 5.1, we talked about including previous observations of a time series as lags. However, there are a few more ways to capture recent and seasonal information using this concept. Let’s take a look.

Lags or backshift

Let’s assume we have a time series with time steps, . Consider that we are at time t and that we have a time series where the length of history is L. So, our time series will have as the latest observation in the time series, and then and so on as we move back in time. So, lags, as explained in Chapter 5, Time Series Forecasting as Regression, are features that include the previous observations in the time series, as shown in the following diagram:

Figure 6.2...