diss.INT.PER {TSclust}

Integrated Periodogram Based Dissimilarity

Description

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.

Author(s)

Pablo Montero Manso, José 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/.

See Also

diss.PER

Examples

## 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)

diss( rbind(x,y,z), "INT.PER", normalize=FALSE )