diss.INT.PER | R Documentation |
Computes the dissimilarity between two time series in terms of the distance between their integrated periodograms.
diss.INT.PER(x, y, normalize=TRUE)
x |
Numeric vector containing the first of the two time series. |
y |
Numeric vector containing the second of the two time series. |
normalize |
If |
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.
The computed distance.
Pablo Montero Manso, José 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. \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.18637/jss.v062.i01")}
diss.PER
## 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 )
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