mvLSW (version 1.0)

Asymp_Quantile: Evaluate the asymptotic quantile of a mvEWS estimate

Description

Evaluate the asymptotic quantile of a multivariate evolutionary wavelet spectrum.

Usage

Asymp_Quantile(object, var = NULL, prob = 0.5, ...)

Arguments

object

A mvLSW object containing the multivariate evolutionary wavelet spectrum estimate.

var

A mvLSW object containing the variance estimate of the wavelet spectrum. This is specified as NULL by default and is evaluated based on object

prob

Probability of length 1 within the range [0,1].

...

Additional arguments to be passed to the varEWS command in calculating the spectral variance.

Value

An object of class mvLSW, invisibly.

Details

This command evaluates the quantile of the asymptotic Gaussian distribution for the mvEWS estimate.

References

Park, T. (2014) Wavelet Methods for Multivariate Nonstationary Time Series, PhD thesis, Lancaster University, pp. 91-111.

See Also

mvEWS, mvLSW, varEWS.

Examples

## Define evolutionary wavelet spectrum, structure only on level 2
Spec <- array(0, dim = c(3, 3, 8, 256))
Spec[1, 1, 2, ] <- 10
Spec[2, 2, 2, ] <- c(rep(5, 64), rep(0.6, 64), rep(5, 128))
Spec[3, 3, 2, ] <- c(rep(2, 128), rep(8, 128))
Spec[2, 1, 2, ] <- Spec[1, 2, 2, ] <- c(rep(0, 64), seq(0, 1, len = 128), rep(1, 64))
Spec[3, 1, 2, ] <- Spec[1, 3, 2, ] <- c(rep(-1, 128), rep(5, 128))
Spec[3, 2, 2, ] <- Spec[2, 3, 2, ] <- -0.5
EWS <- mvLSW(spectrum = Spec, filter.number = 1, family = "DaubExPhase", 
  min.eig.val = NA)

## Sample time series and estimate the EWS.
set.seed(10)
X <- rmvLSW(Spectrum = EWS)
EWS_X <- mvEWS(X, kernel.name = "daniell", kernel.param = 20)

## Evaluate asymptotic spectral variance 
SpecVar <- varEWS(EWS_X)

## Plot Estimate & 95/% confidence interval
Q025 <- Asymp_Quantile(object = EWS_X, var = SpecVar, prob = 0.025)
Q975 <- Asymp_Quantile(object = EWS_X, var = SpecVar, prob = 0.975)
plot(x = EWS_X, style = 2, info = 2, Int.lower = Q025, Int.upper = Q975)