varip2 {locits}

Direct computation of estimate of variance of v_ip, the Haar wavelet coefficients of the periodogram.

Description

Performs a direct computation of an estimate of the variance of the Haar wavelet coefficients of the raw wavelet periodogram of a time series.

Usage

varip2(i, p, ll, S, P)

Arguments

i

Scale parameter of Haar wavelet analyzing periodogram. Scale 1 is the finest scale.

p

Location parameter of Haar wavelet analyzing periodogram

ll

Scale of the raw wavelet periodogram being analyzed

S

Estimate of the spectrum, under the assumption of stationarity. So, this is just a vector of (possibly) J scales (which is often the usual spectral estimate averaged over time). Note: that the main calling function, hwtos2, actually passes maxD levels.

P

Is an autocorrelation wavelet object, returned by the PsiJ function. The wavelet concerned is the analyzing one underlying the raw wavelet periodogram of the series.

Details

Computes the variance of the Haar wavelet coefficients of the raw wavelet periodogram. Note, that this is merely an estimate of the variances.

Value

A list with the following components:

covAA

A component of the variance

covAB

A component of the variance

covBB

A component of the variance

ans

The actual variance

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

Cvarip2,hwtos2, covIwrap

Examples

#
# Generate autocorrelation wavelets
#
P1 <- PsiJ(-5, filter.number=1, family="DaubExPhase")
#
#
# Now compute varip2: this is the variance of the Haar wavelet coefficient
# at the finest scale, location 10 and P1 autocorrelation wavelet.
# Note, I've used S to be the exact coefficients which would be for white noise.
# In practice, S would be an *estimate* calculated from the data.
#
varip2(i=1, p=10, ll=2, S=c(1/2, 1/4, 1/8, 1/16, 1/32), P=P1)
#
# Ans component is 1.865244