pdef {mvLSWimpute}

Function to regularise the LWS matrix.

Description

This function regularises each EWS matrix to ensure that they are strictly positive definite, similar to the mvEWS function in the mvLSW package, except acting on a (bias-corrected) periodogram directly. See mvEWS for more details. Note: this function is not really intended to be used separately, but internally within the spec_estimation function.

Usage

pdef(spec, W = 1e-10)

Arguments

spec

EWS matrix that is to be regularised, can be either a 4D array or a mvLSW object.

W

Tolerance in applying matrix regularisation to ensure each EWS matrix to be strictly positive definite. This is 1e-10 by default.

Value

Returns a mvLSW object containing the regularised EWS of a multivariate locally stationary time series.

Author(s)

Rebecca Wilson

References

Taylor, S.A.C., Park, T.A. and Eckley, I. (2019) Multivariate locally stationary wavelet analysis with the mvLSW R package. _Journal of Statistical Software_ *90*(11) pp. 1-16, doi:10.18637/jss.v090.i11.

Park, T., Eckley, I. and Ombao, H.C. (2014) Estimating time-evolving partial coherence between signals via multivariate locally stationary wavelet processes. _IEEE Transactions on Signal Processing_ *62*(20) pp. 5240-5250.

See Also

mvEWS, spec_estimation

Examples

set.seed(1)
X <- matrix(rnorm(2 * 2^8), ncol = 2)
X[1:2^7, 2] <- 3 * (X[1:2^7, 2] + 0.95 * X[1:2^7, 1])
X[-(1:2^7), 2] <- X[-(1:2^7), 2] - 0.95 * X[-(1:2^7), 1]
X[-(1:2^7), 1] <- X[-(1:2^7), 1] * 4
X <- as.ts(X)

# form periodogram
tmp = apply(X, 2, function(x){haarWT(x)$D})

D = array(t(tmp), dim = c(2, 2^8, 8))

RawPer = array(apply(D, c(2, 3), tcrossprod), dim = c(2, 2, 2^8, 8))
RawPer = aperm(RawPer, c(1, 2, 4, 3))

# now correct

correctedper = correct_per(RawPer)

# now regularize

newper = pdef(correctedper)