The package includes embedded versions of the Mackey-Glass chaotic time series and the Gas Furnance dataset.

**Mackey-Glass chaotic time series**

The Mackey-Glass chaotic time series is defined by the following delayed differential equation:

\(d_x(t) / d_t = (a * x(t - \tau) / (1 + x(t - \tau) ^ 10)) - b * x(t)\)

For this dataset, we generated 1000 samples, with input parameters as follows:

\(a = 0.2\)

\(b = 0.1\)

\(\tau = 17\)

\(x_0 = 1.2\)

\(d_t = 1\)

The dataset is embedded in the following way:

input variables: \(x(t - 18)\), \(x(t - 12)\), \(x(t - 6)\), \(x(t)\)

output variable: \(x(t + 6)\)

**Gas Furnance dataset**

The Gas Furnance dataset is taken from Box and Jenkins. It consists of 292 consecutive values of methane at time \((t - 4)\), and the CO2 produced in a furnance at time \((t - 1)\) as input variables, with the produced CO2 at time \((t)\) as an output variable. So, each training data point consists of \([u(t - 4), y(t - 1), y(t)]\), where \(u\) is methane and \(y\) is CO2.

G. E. P. Box and G. M. Jenkins, "Time series analysis, forecasting and control", San Fransisco, CA: Holden Day (1970).

M. Mackey and L. Glass, "Oscillation and chaos in physiological control systems", Science, vol. 197, pp. 287 - 289 (1977).