The discrete wavelet variance is a useful alternative to the spectral density
function (SDF) and is seen as an octave-band regularization of the SDF. The
wavelet variance decomposes the variance of certain stochastic processes on a
scale-by-scale basis, and thus, is very appealing to the analyst studying
physical phenomena which fluctuate both within and across a wide range of scale.
By definition, the wavelet variance involves an averaged energy summation of
MODWT wavelet coefficients. While DWT wavelet coefficients can also be used, the
statistical properties are inferior to those of the MODWT wavelet variance. See
the references for more details.
REQUIRED ARGUMENTS:
x
A vector containing a uniformly-sampled real-valued time series.
OPTIONAL ARGUMENTS:
transform
A character string denoting the type of wavelet transform: ``modwt" or ``dwt".
Default: ``modwt".
wavelet
A character string denoting the filter type. See wavDaubechies for details.
Default: ``s8".
n.levels
The number of decomposition levels. Default: the maximum level at which there
exists at least one interior wavelet coefficient.
sdf
A vector containing a discretized approximation of the process spectral density
function (SDF). The coefficients of this argument should correspond exactly with
the normalized Fourier frequencies f = [0, 1/P , 2/P, 3/P, ..., (M-1)/P] where P
= 2*(M-1) and M is the number of points in the SDF vector. For example, if the
sdf vector contains five elements, the corresponding frequencies will be f = [0,
1/8, 1/4, 3/8, 1/2]. This argument is used only for calculating mode 2 EDOF. If
the EDOF mode 2 estimates are not desired, send in an empty vector for this
argument and the EDOF mode 2 and corresponding confidence intervals will not be
calculated. Default: empty vector.
sampling.interval
The sampling interval of the time series. Default: 1.
VALUE:
result
An object of class WaveletVariance.
REFERENCES:
(1) D. B. Percival and A. T. Walden, ``Wavelet Methods for Time Series Analysis'',
Cambridge University Press, 2000.
SEE ALSO:
,
,
.
EXAMPLES:
## create sequence
x <- make.signal( "doppler" )
## perform a time independent wavelet variance analysis
vmod <- wavVariance( x )
## plot the results
plot( vmod, pch = 15, title = "Wavelet Variance of Doppler" )
## calculate wavelet variance estimaates for the ocean series
## and calculate EDOF mode 2 estimates and corresponding
## 95 percent confidence intervals
vocean <- wavVariance( ocean, sdf = oceansdf, wavelet = "d6" )
## summarize the results
plot( vocean, edof = 1:3 )
summary( vocean )