locits (version 1.4)

covI: 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.

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.

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