gJADE: Generalized JADE

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/gJADE.R

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

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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

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

k

A vector of lags. It 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

The maximum number of iterations.

method

The method to use for the joint diagonalization. The options are rjd and frjd. Default is frjd.

...

Other arguments passed on to chosen joint diagonalization method.

Details

Assume that a p-variate Y with T observations is whitened, i.e. Y = S^(-1/2)*(X_t - (1/T)*sum_t(X_t)), for t = 1, …, T, where S is the 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 the lagged sample covariance matrix of Y for lag k = 1, …, K, 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

The etimated sources as time series object standardized to have mean 0 and unit variances.

Author(s)

Klaus Nordhausen, Markus Matilainen

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.

See Also

frjd, JADE, gFOBI

Examples

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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

tsBSS documentation built on Aug. 18, 2017, 5:04 p.m.