Beta coefficients in function-on-function regression represent how the predictor function at each point affects the response function at each point. The 3D visualizations on this page allow you to interactively explore the coefficient surfaces. You can:
The plots below show how the previous days’ electricity prices influence current prices throughout the day. The x-axis represents the time of day for the lagged price, while the y-axis represents the time of day for the current price.
Figure 1: Beta coefficient for the one day lagged price.