frbs (version 3.2-0)

# frbsData: Data set of the package

## Description

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

## Details

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.

## References

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).