Rssa (version 1.0)

owcor: Calculate generalized (oblique) W-correlation matrix

Description

Function calculates oblique W-correlation matrix for the series.

Usage

owcor(x, groups, ..., cache = TRUE)

Arguments

x

the input object of `ossa' class

groups

list of numeric vectors, indices of elementary components used for reconstruction. The elementary components must belong to the current OSSA component set

…

further arguments passed to reconstruct routine

cache

logical, if 'TRUE' then intermediate results will be cached in 'ssa' object.

Value

Object of class `wcor.matrix'

Details

Matrix of oblique weighted correlations will be computed. For two series, oblique W-covariation is defined as follows: $$% \mathrm{owcov}(F_1, F_2) = \langle L^\dagger X_1 (R^\dagger)^\mathrm{T}, L^\dagger X_2 (R^\dagger)^\mathrm{T} \rangle_\mathrm{F}, $$ where \(X_1, X_2\) denotes the trajectory matrices of series \(F_1, F_2\) correspondingly, \(L = [U_{b_1} : ... : U_{b_r}], R = [V_{b_1}: ... V_{b_r}]\), where \(\\\{b_1, \dots, b_r\\\}\) is current OSSA component set (see description of `ossa.set' field of `ossa' object), `\(\langle \cdot, \cdot \rangle_\mathrm{F}\)' denotes Frobenius matrix inner product and `\(\dagger\)' denotes Moore-Penrose pseudo-inverse matrix.

And oblique W-correlation is defined the following way: $$% \mathrm{owcor}(F_1, F_2) = \frac{\mathrm{owcov}(F_1, F_2)} {\sqrt{\mathrm{owcov}(F_1, F_1) \cdot \mathrm{owcov(F_2, F_2)}}} $$

Oblique W-correlation is OSSA analogue of W-correlation, that is, a measure of series separability. If I-OSSA procedure separates series exactly, their oblique W-correlation will be equal to zero.

References

Golyandina N. and Shlemov A. (2015): Variations of Singular Spectrum Analysis for separability improvement: non-orthogonal decompositions of time series, Statistics and Its Interface. Vol.8, No 3, P.277-294. http://arxiv.org/abs/1308.4022

See Also

Rssa for an overview of the package, as well as, wcor, iossa, fossa.

Examples

# NOT RUN {
# Separate two non-separable sines
N <- 150
L <- 70

omega1 <- 0.06
omega2 <- 0.065

F <- 4*sin(2*pi*omega1 * (1:N)) + sin(2*pi*omega2 * (1:N))
s <- ssa(F, L)
ios <- iossa(s, nested.groups = list(1:2, 3:4), kappa = NULL, maxIter = 200, tol = 1e-8)

p.wcor <- plot(wcor(ios, groups = list(1:2, 3:4)))
p.owcor <- plot(owcor(ios, groups = list(1:2, 3:4)), main = "OW-correlation matrix")
print(p.wcor, split = c(1, 1, 2, 1), more = TRUE)
print(p.owcor, split = c(2, 1, 2, 1))
# }