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

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.

1 2 3 4 5 6 |

`X` |
Numeric matrix or multivariate time series object of class |

`k` |
Vector of lags. Lag can be any non-negative integer, or a vector consisting of them. Default is |

`eps` |
Convergence tolerance. |

`maxiter` |
Maximum number of iterations. |

`method` |
Method to use for the joint diagonalization, options are |

`...` |
Other arguments passed on to chosen joint diagonalization method. |

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)*.

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. |

Markus Matilainen, Klaus Nordhausen

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
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
``` |

tsBSS documentation built on May 29, 2017, 11:37 p.m.

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