# NSS.TD.JD Method for Nonstationary Blind Source Separation 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`. ```r 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. ## Returns 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. ## References Choi S. and Cichocki A. (2000), Blind separation of nonstationarysources in noisy mixtures, _Electronics Letters_, 36, 848-849. Choi S. and Cichocki A. (2000), Blind separation of nonstationary andtemporally correlated sources from noisy mixtures, Proceedings of the2000 _IEEE Signal Processing Society Workshop Neural Networks forSignal Processing X_, 1, 405-414. Nordhausen K. (2014), On robustifying some second order blind sourceseparation methods for nonstationary time series, _Statistical Papers_,55, 141-156. Miettinen, J., Nordhausen, K. and Taskinen, S. (2017), Blind SourceSeparation Based on Joint Diagonalization in R: The Packages JADE andBSSasymp, _Journal of Statistical Software_, *76*, 1-31,\. ## Author(s) Klaus Nordhausen ## See Also `ts, NSS.JD, NSS.JD, SOBI` ## Examples ```r 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) ```

NSS.TD.JD function