# entropy: Spectral entropy of a time series In tsfeatures: Time Series Feature Extraction

## Description

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

## Usage

 1 entropy(x) 

## Arguments

 x a univariate time series

## Details

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

H_s(x_t) = - \int_{-π}^{π} f_x(λ) \log f_x(λ) d λ,

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

## Value

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

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”. Journal of Machine Learning Research (JMLR) W&CP 28 (2): 64-72, 2013. Available at http://jmlr.org/proceedings/papers/v28/goerg13.html.

spec.ar
 1 2 3 entropy(rnorm(1000)) entropy(lynx) entropy(sin(1:20))