Computes the dissimilarity between two time series in terms of the distance between their integrated periodograms.
Numeric vector containing the first of the two time series.
Numeric vector containing the second of the two time series.
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
The computed distance.
Pablo Montero Manso, Jos<c3><a9> Antonio Vilar.
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/.
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## 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)
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