# diss.INT.PER

##### Integrated Periodogram Based Dissimilarity

Computes the dissimilarity between two time series in terms of the distance between their integrated periodograms.

##### Usage

`diss.INT.PER(x, y, normalize=TRUE)`

##### Arguments

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

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

- normalize
If

`TRUE`

the normalized version is computed.

##### Details

The distance is computed as:
$$ d(x,y) = \int_{-\pi}^{\pi} | F_x(\lambda) - F_y(\lambda) | \, d\lambda, $$
where \( F_x(\lambda_j) = C_x^{-1} \sum_{i=1}^{j} I_x(\lambda_i)\) and \(F_y(\lambda_j) = C_y^{-1} \sum_{i=1}^{j} I_y(\lambda_i)\), with \(C_x = \sum_i I_x(\lambda_i)\) and \(C_y = \sum_i I_y(\lambda_i)\) in the normalized version. \(C_x = 1\) and \(C_y = 1\) in the non-normalized version. \(I_x(\lambda_k)\) and \(I_y(\lambda_k)\) denote the periodograms of `x`

and `y`

, respectively.

##### Value

The computed distance.

##### References

Casado de Lucas, D. (2010) Classification techniques for time series and functional data.

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 three sample time series
x <- cumsum(rnorm(100))
y <- cumsum(rnorm(100))
z <- sin(seq(0, pi, length.out=100))
## Compute the distance and check for coherent results
diss.INT.PER(x, y, normalize=TRUE)
diss.INT.PER(x, y, normalize=TRUE)
diss.INT.PER(x, y, normalize=TRUE)
# }
# NOT RUN {
diss( rbind(x,y,z), "INT.PER", normalize=FALSE )
# }
```

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