The critical D-statistics define the distribution of D for a zero mean Gaussian white noise process. Comparing a D-statistic to the corresponding critical values provides a means of quantitatively rejecting or accepting a linear cumulative energy hypothesis. The table is generated for an ensemble of distribution probabilities and sample sizes.
● Data Source:
CranContrib
● Keywords: distribution
● Alias: D.table.critical
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Given a numeric vector x, this function calculates the the maximum departure of x from an expected linear increase in cumulative energy based on a white noise model.
wavFDPBlock
(Package: wmtsa) :
Block-dependent estimation of fractionally differenced (FD) model parameters
A discrete wavelet transform of the input series is used to calculate block-dependent estimates of the FD parameter, the variance of the FD parameter and the innovations variance. Both a maximum likelihood estimation (MLE) and weighted least squares estimation (WLSE) scheme are supported. If an MLE scheme is chosen, then the DWT is used for its ability to de-correlate long-memory processes. If a WLSE scheme is chosen, then the MODWT is used for its known statistical wavelet variance properties.
The discrete wavelet packet transform (DWPT) contains a multitude of disjoint dyadic decompositions representing an ensemble of different bases. Best basis selection is an attempt to isloate one such basis in an optimal way.
wavMRDSum
(Package: wmtsa) :
Partial summation of a multiresolution decomposition
Forms a multiresolution decomposition (MRD) by taking a specified discrete wavelet transform of the input series and subsequently inverting each level of the transform back to the "time" domain. The resulting components of the MRD form an octave-band decomposition of the original series, and can be summed together to reconstruct the original series. Summing only a subset of these components can be viewed as a denoising operation if the "noisy" components are excluded from the summation.
Let j, t be the decomposition level, and time index, respectively, and s(0,t)=X(t) for t=0,...,N-1 where X(t) is a real-valued uniformly-sampled time series. The jth level MODWT wavelet coefficients d(j,t) and scaling coefficients s(j,t) are defined as d(j,t)=sum(h(l) s(j-1, t - 2^(j-1) l mod N)) and s(j,t)=sum(g(l) s(j-1, t - 2^(j-1) l mod N)) The variable L is the length of both the scaling filter (g) and wavelet filter (h). The d(j,t) and s(j,t) are the wavelet and scaling coefficients, respectively, at decomposition level j and time index t. The MODWT is a collection of all wavelet coefficients and the scaling coefficients at the last level: d(1),d(2),...,d(J),s(J) where d(j) and s(j) denote a collection of wavelet and scaling coefficients, respectively, at level j.
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