diss.ACF: Autocorrelation-based Dissimilarity

Description

Computes the dissimilarity between two time series as the distance between their estimated simple (ACF) or partial (PACF) autocorrelation coefficients.

Usage

diss.ACF(x, y, p = NULL, omega=NULL, lag.max=50)
diss.PACF(x, y, p = NULL, omega=NULL, lag.max=50)

Arguments

Numeric vector containing the first of the two time series.

Numeric vector containing the second of the two time series.

If not NULL, sets the weight for the geometric decaying of the autocorrelation coefficients. Ranging from 0 to 1.

lag.max

Maximum number of simple or partial autocorrelation coefficients to be considered.

omega

If not NULL, completely specifies the weighting matrix for the autocorrelation coefficients. p is ignored if omega is used.

Value

The computed distance.

Details

Performs the weighted Euclidean distance between the simple autocorrelation ( dist.ACF) or partial autocorrelation ( dist.PACF ) coefficients. If neither p nor omega are specified, uniform weighting is used. If p is specified, geometric wights decaying with the lag in the form $ p(1-p)^i$ are applied. If omega ($\Omega$) is specified, $$ d(x,y) = {\{ ( \hat{\rho}_{x} - \hat{\rho}_{y} )^t \bm{\Omega} (\hat{\rho}_{x} - \hat{\rho}_{y} ) \}}^\frac{1}{2} $$ with $\hat{\rho}_{x}$ and $\hat{\rho}_{y}$ the respective (partial) autocorrelation coefficient vectors.

References

Galeano, P. and Pe<U+00F1>a, D. (2000). Multivariate analysis in vector time series. Resenhas, 4 (4), 383--403.

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/.

Examples

Run this code

# NOT RUN {
## 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.PACF(x, y)
diss.ACF(x, z)
diss.PACF(y, z)
#create a dist object for its use with clustering functions like pam or hclust
diss( rbind(x,y,z), "ACF", p=0.05)

# }

Run the code above in your browser using DataCamp Workspace