holderSpectrum(wmtsa)
holderSpectrum()所属R语言包：wmtsa
The Holder spectrum of a time series
持有频谱的时间序列
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Using a tree, this function returns time localized exponent
使用一棵树，这个函数返回的时间本地化指数
用法----------Usage----------
holderSpectrum(x, n.scale.min=3, fit=lmsreg)
参数----------Arguments----------
参数：x
an object of class wavCWTTree.
对象类wavCWTTree。
参数：fit
a linear regression function to use in fitting the resulting data. Default: lmsreg.
在嵌合所产生的数据使用一个线性回归函数。默认值：lmsreg。
参数：n.scale.min
the minimum number of scales (points) that a given suitable branch segment must have before being considered as an admissible candidate for exponent estimation. Default: 3.
尺度的最小数目（点数），一个给定的合适的分支段必须具有被视为受理候选人指数估计之前。默认值：3。
Details
详细信息----------Details----------
Many real-world time series contain sharp dicontinuities (cusps) which can be attributed to rapid changes in the observed system. These cusps are called singularities and their strength can be quantified via localized exponents as follows: Let f(t) be a continuous real-valued function containing a singularity at time t0. The exponent h(t0) is defined as the supremum (least upper bound) of all exponents h which satisfies the condition
许多真实世界的时间系列包含尖锐dicontinuities，（齿尖），它可以归因于快速变化的观察系统。这些尖点被称为奇点自己的实力可以量化的通过本地化指数的如下：让f(t)是一个连续的实值函数，其中包含一个奇点时t0。的指数h(t0)被定义为所有指数的上确界（最小上界）h满足条件
Thus, the strength of cusp singularities in a given time series can be quantified by
因此，尖奇异性的强度，可以量化的在一个给定的时间序列
iCalculate the CWT of the time series.
iCalculate CWT的时间序列。
iiFind the modulus maxima of the CWT (WTMM).
iiFind CWT（WTMM）的模极大值。
iiiLink the WTMM into separate branches based (mainly) on their position in time to form a WTMM tree.
iiiLink WTMM到基于单独的分支（主要），对它们的位置的时间，以形成WTMM树。
ivFor each branch in the tree, perform an exponential fit of the WTMM over an admissible range of scale and as the scale approaches zero. The resulting scaling exponent is an estimate of the local exponent for the time series. The occurrence of the singularity in time is recorded as the location in time where the WTMM converges as the scale nears zero.
ivFor在树的每个分支，指数拟合的WTMM的允许范围内的规模和规模趋近于零。将得到的标度指数是一个估计值的时间序列的本地指数。时间中的奇异性的发生被记录作为时间的位置，其中WTMM收敛作为秤接近为零。
In practice, the above technique can be unstable when applied to observational data due to negative moment divergences and so-called outliers which correspond to the end points of sample singularities. One must also be very careful in selecting an appropriate scaling region of a tree branch before fitting the data. We accomplish this by first segmenting a given tree branch into regions which exhibit approximate linear behavior in the log(scale)-log(WTMM) space, and subsequently selecting the region corresponding to the smallest scales for exponent estimation. Furthermore, through the n.scale.min argument, the user can control the minimum number of scales (points) that must exist in the isolated scaling region before a exponent estimation is recorded.
在实践中，上述技术可以是不稳定的，当应用到由于负弯矩分歧和所谓的离群值对应样本奇点的结束点的观测数据。也必须非常小心地选择适当的缩放区域的一根树枝装修前的数据。我们完成，这首先通过一个给定的树枝分割成区域具有近似线性的行为在log中（尺度）log（WTMM）的空间，并随后选择的区域对应的指数估计的最小尺度。此外，用户可以通过n.scale.min参数，控制尺度的最小数目（点数），必须存在于分离的缩放区域之前指数估计记录。
值----------Value----------
a list containing the estimated exponents, associated times and corresponding branch number.
一个列表，其中包含估计指数，相关的时间和相应的分支数。
参考文献----------References----------
S.G. Mallat, A Wavelet Tour of Signal Processing (2nd Edition), Academic Press, Cambridge, 1999.
S.G. Mallat and W.L. Hwang, “Singularity detection and processing with wavelets", IEEE Transactions on Information Theory, 38, 617–643 (1992).
S.G. Mallat and S. Zhong, “Complete signal representation with multiscale edges", IEEE Transactions on Pattern Analysis and Machine Intelligence, 14, 710–732 (1992).
J.F. Muzy, E. Bacry, and A. Arneodo, “The multifractal formalism revisited with wavelets.", International Journal of Bifurcation and Chaos, 4, 245–302 (1994).
参见----------See Also----------
实例----------Examples----------
## create series with a linear trend and two [＃创建一系列的线性趋势和]
## cusps: h(x = 1) = 0.5 and h(x = 15) = 0.3 [＃尖点：小时（x = 1时）= 0.5和h（= 15）= 0.3]
cusps <- function(x) -0.2 * abs(x-1)^0.5 - 0.5* abs(x-15)^0.3 + 0.00346 * x + 1.34
x <- seq(-5, 20, length=1000)
y <- signalSeries(cusps(x), x)
## calculate CWT using Mexican hat filter [＃计算CWT利用墨西哥帽过滤器]
W <- wavCWT(y, wavelet="gaussian2")
## calculate WTMM and extract first two branches [＃计算的WTMM和提取前两个分支]
## in tree corresponding to the cusps [＃树的尖点]
W.tree <- wavCWTTree(W)[1:2]
## plot the CWT tree overlaid with a scaled [＃图规模较小的的CWT树覆盖有]
## version of the time series to illustrate [＃版本的时间序列说明]
## alignment of branches with cusps [＃对准与牙尖的分支]
yshift <- y@data - min(y@data)
yshift <- yshift / max(yshift) * 4 - 4.5
plot(W.tree, xlab="x")
lines(x, yshift, lwd=2)
text(6.5, -1, "f(x) = -0.2|x-1|^0.5 - 0.5|x-15|^0.3 + 0.00346x + 1.34", cex=0.8)
## estimate Holder exponents [估计持有人指数]
holder <- holderSpectrum(W.tree)
print(holder)
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
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发表于 2012-10-1 22:50:26
