R Graphical Manual

Browse All

Last data update: 2014.03.03

R: Generalized JADE

gJADE

R Documentation

Generalized JADE

Description

The gJADE method for blind source separation problem. It is designed for time series with stochastic volatility. The method is a generalization of JADE, which is a method for blind source separation problem using only marginal information.

Usage

gJADE(X, ...)

## Default S3 method:
gJADE(X, k = 0:12, eps = 1e-06, maxiter = 100, method = "frjd", ...)
## S3 method for class 'ts'
gJADE(X, ...)

Arguments

`X`	Numeric matrix or multivariate time series object of class `ts`. Missing values are not allowed.
`k`	Vector of lags. Lag can be any non-negative integer, or a vector consisting of them. Default is `0:12`. If k = 0, this method reduces to `JADE`.
`eps`	Convergence tolerance.
`maxiter`	Maximum number of iterations.
`method`	Method to use for the joint diagonalization, options are `rjd` and `frjd`. Default is `frjd`.
`...`	Other arguments passed on to chosen joint diagonalization method.

Details

Assume that Y has p columns and it is whitened, i.e. Y = S^(-1/2)*(X - (1/T)*sum_t(X_(ti))), where S is a sample covariance matrix of X. The matrix C^ij_k(Y) is of the form

C^ij_k(Y) = B^ij_k(Y) - S_k(Y) (E^ij + E^ji) S_k(Y)' - trace(E^ij)*I,

for i, j = 1, …, p, where S_k(Y) is a lagged sample covariance matrix of Y, E^ij is a matrix where element (i,j) equals to 1 and all other elements are 0, I is an identity matrix of order p and B^ij_k(Y) is as in gFOBI.

The algorithm finds an orthogonal matrix U by maximizing

sum_i(sum_j (sum_k (||diag(U C^ij_k(Y) U')||^2))),

where k = 1, …, K. The final unmixing matrix is then W = U S^(-1/2).

Value

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

`W`	The estimated unmixing matrix.
`k`	The vector of the used lags.
`S`	Estimated sources as time series object standardized to have mean 0 and unit variances.

Author(s)

Klaus Nordhausen

References

Cardoso, J.-F., Souloumiac, A., (1993). Blind beamforming for non-Gaussian signals, in: IEE-Proceedings-F, volume 140, pp. 362–370.

Matilainen, M., Nordhausen, K. and Oja, H. (2015), New independent component analysis tools for time series, Statistics & Probability Letters, 105, 80–87.

Examples

library(stochvol)
n <- 10000
A <- matrix(rnorm(9), 3, 3)

# simulate SV models
s1 <- svsim(n, mu = -10, phi = 0.8, sigma = 0.1)$y
s2 <- svsim(n, mu = -10, phi = 0.9, sigma = 0.2)$y
s3 <- svsim(n, mu = -10, phi = 0.95, sigma = 0.4)$y

X <- cbind(s1, s2, s3) %*% t(A)

res <- gJADE(X)
res
coef(res)
plot(res)
head(bss.components(res))

MD(res$W, A) # Minimum Distance Index, should be close to zero