NSS.TD.JD {JADE}

NSS.TD.JD Method for Nonstationary Blind Source Separation

Description

The NSS.TD.JD method for nonstationary blind source separation. The method first whitens the complete data and then divides it into K time intervals. It is then assumed that within each interval the time series is approximately second order stationary and within each interval L autocovariance are computed. The underlying sources are then found by jointly diagonalizing the K*L autocovariance matrices using frjd.

Usage

NSS.TD.JD(X, ...)

## Default S3 method:
NSS.TD.JD(X, K=12, Tau=0:11, n.cuts=NULL, eps = 1e-06, maxiter = 100, ...)
## S3 method for class 'ts'
NSS.TD.JD(X, ...)

Arguments

X

a numeric matrix or a multivariate time series object of class ts. Missing values are not allowed.

K

number of intervals to be used.

Tau

Lags for the autovariance matrices to be computed within each interval.

n.cuts

if NULL, then the time series is divided into K equally long intervals. To specify intervals n.cuts should be given in the form c(1,n.cut.1,...,n.cut.k, nrow(X)) to specify where to split the time series.

eps

maximum number of iterations for frjd.

maxiter

convergence tolerance for frjd.

...

further arguments to be passed to or from methods.

Details

The model assumes that the mean of the p-variate time series is constant but the variances change over time.

Value

A list with class 'bss' containing the following components:

W

estimated unmixing matrix.

k

the lags used for the autocovariance matrix used in each interval.

n.cut

specifying the intervals where data is split

K

the number of intervals used

S

estimated sources as time series objected standardized to have mean 0 and that the sources 1.

Author(s)

Klaus Nordhausen

References

Choi S. and Cichocki A. (2000), Blind separation of nonstationary sources in noisy mixtures, Electronics Letters, 36, 848–849.

Choi S. and Cichocki A. (2000), Blind separation of nonstationary and temporally correlated sources from noisy mixtures, Proceedings of the 2000 IEEE Signal Processing Society Workshop Neural Networks for Signal Processing X, 1, 405–414.

Nordhausen K. (2014), On robustifying some second order blind source separation methods for nonstationary time series, Statistical Papers, 55, 141–156.

Miettinen, J., Nordhausen, K. and Taskinen, S. (2017), Blind Source Separation Based on Joint Diagonalization in R: The Packages JADE and BSSasymp, Journal of Statistical Software, 76, 1–31, <doi:10.18637/jss.v076.i02>.

See Also

ts, NSS.JD, NSS.JD, SOBI

Examples

n <- 1000
s1 <- rnorm(n)
s2 <- 2*sin(pi/200*1:n)* rnorm(n)
s3 <- c(rnorm(n/2), rnorm(100,0,2), rnorm(n/2-100,0,1.5))
S <- cbind(s1,s2,s3)
plot.ts(S)
A<-matrix(rnorm(9),3,3)
X<- S%*%t(A)

NSS3 <- NSS.TD.JD(X)
NSS3
MD(coef(NSS3),A)
plot(NSS3)
cor(NSS3$S,S)

NSS3b <- NSS.TD.JD(X, Tau=c(0,3,7,12), K=6)
MD(coef(NSS3b),A)

NSS3c <- NSS.TD.JD(X, n.cuts=c(1,300,500,600,1000))
MD(coef(NSS3c),A)