# Evaluate the Approximate Confidence Interval of a mvEWS Estimate Evaluate the approximate confidence interval of a multivariate evolutionary wavelet spectrum. methods ```r 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 ```r ## 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) ```

ApxCI function