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

The gFOBI method for blind source separation problem. It is designed for 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` |
A numeric matrix or a multivariate time series object of class |

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

`eps` |
Convergence tolerance. |

`maxiter` |
The maximum number of iterations. |

`method` |
The method to use for the joint diagonalization. The options are |

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

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*. 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 ` |
The 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 Aug. 18, 2017, 5:04 p.m.

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.