# diss.SPEC.ISD

##### Dissimilarity Based on the Integrated Squared Difference between the Log-Spectra

Computes the dissimilarity between two time series in terms of the integrated squared difference between non-parametric estimators of their log-spectra.

##### Usage

`diss.SPEC.ISD(x, y, plot=FALSE, n=length(x))`

##### Arguments

- x
Numeric vector containing the first of the two time series.

- y
Numeric vector containing the second of the two time series.

- plot
If

`TRUE`

, plot the smoothed spectral densities of the two series.- n
The number of points to use for the linear interpolation. A value of n=0 uses numerical integration instead of linear interpolation. See details.

##### Details

$$ d(x,y) = \int ( \hat{m}_x(\lambda) - \hat{m}_y(\lambda))^2 \, d\lambda, $$ where \( \hat{m}_x(\lambda) \) and \( \hat{m}_y(\lambda) \) are local linear smoothers of the log-periodograms, obtained using the maximum local likelihood criterion.

By default, for performance reasons, the spectral densities are estimated using linear interpolation using `n`

points. If `n`

is 0, no linear interpolation is performed, and `integrate`

is used to calculate the integral, using as many points as `integrate`

sees fit.

##### Value

The computed distance.

##### References

P<U+00E9>rtega, S. and Vilar, J.A. (2010) Comparing several parametric and nonparametric approaches to time series clustering: A simulation study. *J. Classification*, **27(3)**, 333--362.

Montero, P and Vilar, J.A. (2014) *TSclust: An R Package for Time Series Clustering.* Journal of Statistical Software, 62(1), 1-43. http://www.jstatsoft.org/v62/i01/.

##### See Also

##### Examples

```
# NOT RUN {
## Create two sample time series
x <- cumsum(rnorm(50))
y <- cumsum(rnorm(50))
z <- sin(seq(0, pi, length.out=50))
## Compute the distance and check for coherent results
diss.SPEC.ISD(x, y, plot=TRUE)
#create a dist object for its use with clustering functions like pam or hclust
# }
# NOT RUN {
diss.SPEC.ISD(x, y, plot=TRUE, n=0)#try integrate instead of interpolation
diss( rbind(x,y,z), "SPEC.ISD" )
# }
# NOT RUN {
# }
```

*Documentation reproduced from package TSclust, version 1.2.4, License: GPL-2*