correct_per {mvLSWimpute}

Function to smooth the raw wavelet periodogram

Description

This function corrects the raw wavelet periodogram, similar to the mvEWS function in the mvLSW package, except acting on the raw 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

correct_per(RawPer)

Arguments

RawPer

Raw wavelet periodogram that is to be corrected, can be either a 4D array or a mvLSW object.

Details

The raw wavelet periodogram as an estimator for the local wavelet spectrum (LWS) is biased, and thus needs to be corrected. This is done using a correction (debiasing) matrix, formed from the inner product of autocorrelation wavelets, see Park et al. (2014), Taylor et al. (2019) for more details. This function performs this bias-correction.

Value

Returns a mvLSW object containing the smoothed 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

## Sample bivariate locally stationary time series

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, reshaping array as necessary

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)