covI {locits}

Compute the covariance between two wavelet periodogram ordinates at the same scale, but different time locations.

Description

Computes cov(I_{\ell, m}, I_{\ell, n}) using the formula given in Nason (2012) in Theorem 1. Note: one usually should use the covIwrap function for efficiency.

Usage

covI(II, m, n, ll, ThePsiJ)

Arguments

II

Actually the *spectral* estimate S, not the periodogram values. This is for an assumed stationary series, so this is just a vector of length J, one for each scale of S.

m

Time location m

n

Time location n

ll

Scale of the raw wavelet periodogram

ThePsiJ

Autocorrelation wavelet corresponding to the wavelet that computed the raw peridogram (also assumed to underlie the time series

Value

The covariance is returned.

Author(s)

Guy Nason.

References

Nason, G.P. (2013) A test for second-order stationarity and approximate confidence intervals for localized autocovariances for locally stationary time series. J. R. Statist. Soc. B, 75, 879-904. doi:10.1111/rssb.12015

See Also

covIwrap

Examples

P1 <- PsiJ(-5, filter.number=1, family="DaubExPhase")
#
# Compute the covariance
#
covI(II=c(1/2, 1/4, 1/8, 1/16, 1/32), m=1, n=3, ll=5, ThePsiJ=P1)
#
# [1] 0.8430809