TSclust (version 1.1)

diss.INT.PER: 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.

Value

• The computed distance.

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.

References

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

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)
proxy::dist( rbind(x,y,z), diss.INT.PER, normalize=FALSE )