entropy {tsfeatures}

Spectral entropy of a time series

Description

Computes spectral entropy from a univariate normalized spectral density, estimated using an AR model.

Usage

entropy(x)

Arguments

x

a univariate time series

Details

The spectral entropy equals the Shannon entropy of the spectral density f_x(\lambda) of a stationary process x_t:

H_s(x_t) = - \int_{-\pi}^{\pi} f_x(\lambda) \log f_x(\lambda) d \lambda,

where the density is normalized such that \int_{-\pi}^{\pi} f_x(\lambda) d \lambda = 1. An estimate of f(\lambda) can be obtained using spec.ar with the burg method.

Value

A non-negative real value for the spectral entropy H_s(x_t).

Author(s)

Rob J Hyndman

References

Jerry D. Gibson and Jaewoo Jung (2006). “The Interpretation of Spectral Entropy Based Upon Rate Distortion Functions”. IEEE International Symposium on Information Theory, pp. 277-281.

Goerg, G. M. (2013). “Forecastable Component Analysis”. Proceedings of the 30th International Conference on Machine Learning (PMLR) 28 (2): 64-72, 2013. Available at https://proceedings.mlr.press/v28/goerg13.html.

See Also

spec.ar

Examples

entropy(rnorm(1000))
entropy(lynx)
entropy(sin(1:20))