In ahaeusser/echos: Echo State Networks for Time Series Modeling and Forecasting

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.height = 5,
  fig.width = 7
)

Load package

library(echos)

Prepare dataset

In a first example, we want to model the well-known AirPassenger time series (ts object). The dataset contains monthly totals of international airline passengers (in thousands) from January 1949 to December 1960 with 144 observations in total. The first 132 observations are used for model training (n_train) and last 12 observations are used for testing (n_ahead). xtrain and xtest are numeric vectors containing the training and testing data.

# Forecast horizon
n_ahead <- 12
# Number of observations (total)
n_obs <- length(AirPassengers)
# Number of observations (training data)
n_train <- n_obs - n_ahead

# Prepare train and test data as numeric vectors
xtrain <- AirPassengers[(1:n_train)]
xtest <- AirPassengers[((n_train+1):n_obs)]

xtrain
xtest

Train ESN model

The function train_esn() is used to automatically train an ESN to the input data xtrain, where the output xmodel is an object of class esn. The object xmodel is a list containing the actual and fitted values, residuals, the internal states states_train, estimated coefficients from the ridge regression estimation, hyperparameters, etc. We can summarize the model by using the generic S3 method summary() to get detailed information on the trained model.

# Train ESN model
xmodel <- train_esn(y = xtrain)

# Plot actual and fitted values
plot(xmodel$actual, type = "l")
lines(xmodel$fitted, col = "steelblue", lwd = 2)

# Summarize model
summary(xmodel)

From the output above, we get the following information about the trained ESN model:

| Value | Description | |:-----------------|:---------------------------------------------------------------------------------------------------------------| | n_obs | Number of observations (i.e., length of the input time series) | | n_diff | Number of differences required to achieve (weak-) stationarity of the input training data | | lags | Lags of the output variable (response), which are used as model input | | n_states | Number of internal states (i.e., predictor variables or reservoir size). | | alpha | Leakage rate (smoothing parameter) | | rho | Spectral radius for scaling the reservoir weight matrix | | density | Density of the reservoir weight matrix | | scale_inputs | Input training data are scaled to the interval (-0.5, 0.5) | | scale_win | Input weights matrix is drawn from a random uniform distribution with interval (-0.5, 0.5) | | scale_wres | Reservoir weight matrix is drawn from a random uniform distribution with interval (-0.5, 0.5) | | n_models | Number of models evaluated during the random search optimization to find the regularization parameter lambda | | df | Effective degrees of freedom in the model | | lambda | Regularization parameter for the ridge regression estimation |

Forecast ESN model

The function forecast_esn() is used to forecast the trained model xmodel for n_ahead steps into the future. The output xfcst is a list of class forecast_esn containing the point forecasts, actual and fitted values, the forecast horizon n_ahead and the model specification model_spec. We can use the generic S3 method plot() to visualize the point forecast within xfcst and add the holdout test data xtest.

# Forecast ESN model
xfcst <- forecast_esn(xmodel, n_ahead = n_ahead)
xfcst

# Plot forecast and test data
plot(xfcst, test = xtest)

ahaeusser/echos documentation built on June 2, 2025, 2:17 a.m.