wavVarConfidence: Wavelet variance confidence intervals

Description

This function calculates wavelet variance confidence intervals for the unbiased and block averaged discrete wavelet variance estimates. Given $\hat\nu_X^2(\tau_j)$ are the time independent unbiased wavelet variance estimates at scales $\tau_j\equiv 2^{j-1}$ where $j$ are the decomposition levels, the approximate $100(1-2p)$% confidence interval is given by $$ \biggl[{ n\hat\nu_X^2(\tau_j) \over Q_n(1-p) } , { n\hat\nu_X^2(\tau_j) \over Q_n(p) } \biggr] $$ where $Q_n(p)$ is the $p \times 100$ percentage point for a chi-squared distribution with n degrees of freedom distribution.

Usage

wavVarConfidence(wvar, edof, probability=0.95)

Arguments

wvar

a vector containing the block-averaged unbiased wavelet variance estimates.

edof

a vector containing the equivalent degrees of freedom estimates. See wavEDOF for details.

probability

the probability desired for the confidence intervals. Supported probabilities are 0.005, .025, .05, .95, .975, and .995. Default: 0.95.

Value

a list of the low and high confidence interval limits for levels $1,\ldots, J$.

References

D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000.

Examples

Run this code

# NOT RUN {
## first calculate the EDOF for the ocean series 
edof <- wavEDOF(ocean)

## calculate the 95% confidence intervals for EDOF 
## mode 1 
wavVarConfidence(edof$variance.unbiased, edof$EDOF1)
# }