ApxCI function

Evaluate the Approximate Confidence Interval of a mvEWS Estimate

Evaluate the approximate confidence interval of a multivariate evolutionary wavelet spectrum. methods

ApxCI(object, var = NULL, alpha = 0.05, ...)

Arguments

• object: A mvLSW object containing the multivariate evolutionary wavelet spectrum estimate.
• var: A mvLSW object containing the variance estimate of the wavelet spectrum. If this is NULL (default) then the variance is estimates by calling the varEWS and using object.
• alpha: Type I error, a single numerical value within (0,0.5].
• ...: Additional arguments to be passed to the varEWS command.

Details

The command evaluates the approximate Gaussian confidence intervals for the elements of the mvEWS estimate.

Returns

Invisibly returns a list containing two mvLSW classed objects with names "L" and "U" that respectively identify the lower and upper interval estimates.

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

See Also

mvEWS, as.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, ] <- punif(1:256, 65, 192)
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 <- as.mvLSW(x = 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
CI <- ApxCI(object = EWS_X, var = SpecVar, alpha = 0.05)
plot(x = EWS_X, style = 2, info = 2, Interval = CI)