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Last data update: 2014.03.03

R: Generalized FOBI

gFOBI

R Documentation

Generalized FOBI

Description

The gFOBI method for blind source separation problem. It is used in case of time series with stochastic volatility. The method is a generalization of FOBI, which is a method designed for iid data.

Usage

gFOBI(X, ...)

## Default S3 method:
gFOBI(X, k = 0:12, eps = 1e-06, maxiter = 100, method = "frjd", ...)
## S3 method for class 'ts'
gFOBI(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 `FOBI`.
`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. Algorithm first calculates

B^ij_k(Y) = (1/(T - k))*sum[Y_(t + k) Y_t' E^ij Y_t Y_(t + k)'],

where t = 1, …, T, and then

B_k(Y) = sum(B^ii_k(Y)),

for i = 1, …, p.

The algorithm finds an orthogonal matrix U by maximizing

sum(||diag(U B_k(Y) U')||^2).

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)

Markus Matilainen, Klaus Nordhausen

References

Cardoso, J.-F., (1989), Source separation using higher order moments, in: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, 2109–2112.

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

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