Figure 3
From: Forecasting high-dimensional dynamics exploiting suboptimal embeddings
Forecast profile of the Lorenz’96I model with the data length of 4000. Panel (a) shows the proportion of embedding of the proposed forecasts. The color indicates the proportion of embedding for each variable averaged over the number of combined forecasts for each step. Note that for each prediction step, the sum of the proportions of all variables is one. Variables \({x}_{0},\ldots ,{x}_{4}\) are the variables of the 10-dimensional Lorenz’96I equations, and the other variables are random walks. Panel (b) shows the averaged filter coefficient ρ and embedding dimension E over the combined forecasts for each step. Note that the averaged dimensions can be a decimal fraction since they are averaged over the number of combined forecasts for each step. Panel (c) shows the relation between the number of combined forecasts and the errors. The solid line shows the in-sample error, and the dashed line shows the test error. The vertical solid line shows the selected number of combined forecasts kp to minimize the in-sample error.
