This function calculates wavelet variance confidence intervals
for the unbiased and block averaged discrete wavelet variance estimates.
Given $var{tau(j)}$ are the
time independent unbiased wavelet variance estimates at scales
$tau(j)$ 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 $Q(p)$ is the
$p x 100$ 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 $1,..., J$.
References
D. B. Percival and A. T. Walden,
Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000.
## 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)