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

## Arguments

- x
a univariate time series

## Value

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

## 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.

## 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.

## Examples

```
entropy(rnorm(1000))
#> entropy
#> 1
entropy(lynx)
#> entropy
#> 0.7331515
entropy(sin(1:20))
#> entropy
#> 0.003481715
```