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# echos <img src="man/figures/logo.png" align="right" height="139" alt="" />

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The `echos` package provides a comprehensive set of **functions and
methods** for modeling and forecasting univariate time series using
**Echo State Networks (ESNs)**. It offers two alternative approaches:

- **Base R interface:** Functions for modeling and forecasting time
  series using `numeric` vectors, allowing for straightforward
  integration with existing R workflows.
- **Tidy interface:** A seamless integration with the
  [`fable`](https://github.com/tidyverts/fable) framework based on
  [`tsibble`](https://github.com/tidyverts/tsibble), enabling tidy time
  series forecasting and model evaluation. This interface leverages the
  [`fabletools`](https://github.com/tidyverts/fabletools) package,
  providing a consistent and streamlined workflow for model development,
  evaluation, and visualization.

The package features a **lightweight implementation** that enables
**fast and automatic** model training and forecasting using ESNs. You
can quickly and easily build accurate ESN models without requiring
extensive hyperparameter tuning or manual configuration.

## Model specification

`echos` implements Echo State Networks with a fixed randomly initialized
reservoir and a ridge-regression readout. The input and reservoir
weights are generated once and kept fixed, while only the readout layer
is estimated.

The main ESN hyperparameters are the reservoir size (`n_states`),
leakage rate (`alpha`), spectral radius (`rho`), reservoir density
(`density`), input scaling (`scale_inputs`, `scale_win`, `scale_wres`),
and the ridge regularization range (`lambda`). These parameters control
the memory, stability, complexity, and regularization of the model.

By default, `train_esn()` automatically determines the number of
differences, constructs the reservoir, evaluates candidate ridge readout
models, and selects the final readout using an information criterion.
For explicit grid-based tuning of `alpha`, `rho`, and `tau`, use
`tune_esn()`.

## Installation

You can install the **stable** version from
[CRAN](https://cran.r-project.org/package=echos):

``` r
install.packages("echos")
```

You can install the **development** version from
[GitHub](https://github.com/):

``` r
# install.packages("devtools")
devtools::install_github("ahaeusser/echos")
```

## Base R

``` r
library(echos)

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

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

# Train and forecast ESN model
xmodel <- train_esn(y = xtrain)
xfcst <- forecast_esn(xmodel, n_ahead = n_ahead)

# Plot result
plot(xfcst, test = xtest)
```

<img src="man/figures/README-base-1.svg" alt="Plot forecast and test data" width="100%" />

## Tidy R

``` r
library(echos)
library(tidyverse)
library(tsibble)
library(fable)

# Prepare train data
train_frame <- m4_monthly_subset %>%
  filter(series %in% c("M21655", "M2717"))

# Train and forecast ESN model
train_frame %>%
  model(
    "ESN" = ESN(value),
    "ARIMA" = ARIMA(value)
    ) %>%
  forecast(h = 18) %>%
  autoplot(train_frame, level = NULL)
```

<img src="man/figures/README-tidy-1.svg" alt="Plot forecast and train data" width="100%" />

## Links

- [CRAN](https://cran.r-project.org/package=echos)
- [Website](https://ahaeusser.github.io/echos/)

## References

- Häußer, A. (2026). *Echo State Networks for Time Series Forecasting:
  Hyperparameter Sweep and Benchmarking.* arXiv preprint
  arXiv:2602.03912. <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* (2nd ed.),
  pp. 659–686. Springer.
- Lukosevicius, M., & Jaeger, H. (2009). *Reservoir computing approaches
  to recurrent neural network training.* *Computer Science Review*,
  3(3), 127–149.
