diss.INT.PER: Integrated Periodogram Based Dissimilarity In TSclust: Time Series Clustering Utilities

Description

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

Usage

 `1` ```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( F_x(λ) - F_y(λ))dλ | λ = -π to π

where F_x(λ_j)=(sum F_x(λ_i)|i=1 to j)/C_x and F_y(λ_j)=(sum F_y(λ_i)|i=1 to j)/C_xy, with C_x = ∑_i I_x(λ_i) and C_y = ∑_i I_y(λ_i) in the normalized version. C_x = 1 and C_y = 1 in the non-normalized version. I_x(λ_k) and I_y(λ_k) denote the periodograms of `x` and `y`, respectively.

Value

The computed distance.

Author(s)

Pablo Montero Manso, Jos<c3><a9> Antonio Vilar.

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/.

`diss.PER`

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```## 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 ) ## End(Not run) ```

Example output

```Loading required package: wmtsa
Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE