forecast_esn: Forecast an Echo State Network

Description

Forecast an Echo State Network (ESN) from a trained model via recursive forecasting. Forecast intervals are generated by simulating future sample path based on a moving block bootstrap of the residuals and estimating the quantiles from the simulations.

Usage

forecast_esn(
  object,
  n_ahead = 18,
  levels = c(80, 95),
  n_sim = 100,
  n_seed = 42
)

Value

A list containing:

point: Numeric vector containing the point forecasts.
interval: Numeric matrix containing the forecast intervals.
sim: Numeric matrix containing the simulated future sample path.
std: Numeric vector with standard deviations.
levels: Integer vector. The levels of the forecast intervals.
actual: Numeric vector containing the actual values.
fitted: Numeric vector containing the fitted values.
n_ahead: Integer value. The number of periods for forecasting (forecast horizon).
model_spec: Character value. The model specification as string.

Arguments

object: An object of class esn. The result of a call to train_esn().
n_ahead: Integer value. The number of periods for forecasting (i.e. forecast horizon).
levels: Numeric vector. The levels of the forecast intervals (in percent), e.g., c(80, 95). Values must lie between 0 and 100.
n_sim: Integer value. The number of simulated future paths used to compute forecast intervals via a moving block bootstrap of the (demeaned) in-sample residuals. If NULL, no intervals are computed.
n_seed: Integer value. The seed for the random number generator (for reproducibility).

References

Häußer, A. (2026). Echo State Networks for Time Series Forecasting: Hyperparameter Sweep and Benchmarking. arXiv preprint arXiv:2602.03912, 2026. https://arxiv.org/abs/2602.03912
Jaeger, H. (2001). The “echo state” approach to analysing and training recurrent neural networks with an erratum note. Bonn, Germany: German National Research Center for Information Technology GMD Technical Report, 148(34):13.
Jaeger, H. (2002). Tutorial on training recurrent neural networks, covering BPPT, RTRL, EKF and the "echo state network" approach.
Lukosevicius, M. (2012). A practical guide to applying echo state networks. In Neural Networks: Tricks of the Trade: Second Edition, pages 659–686. Springer.
Lukosevicius, M. and Jaeger, H. (2009). Reservoir computing approaches to recurrent neural network training. Computer Science Review, 3(3):127–149.

Examples

Run this code

xdata <- as.numeric(AirPassengers)
xmodel <- train_esn(y = xdata)
xfcst <- forecast_esn(xmodel, n_ahead = 12)
plot(xfcst)