The D-statistic denotes the maximum
deviation of sequence from a hypothetical linear cumulative energy
trend. The critical D-statistics define the distribution of D for a
zero mean Gaussian white noise process. Comparing the sequence
D-statistic to the corresponding critical
values provides a means of quantitatively rejecting or accepting the
linear cumulative energy hypothesis. The table is generated for an
ensemble of distribution probabilities and sample sizes.
D.table(n.sample=c(127, 130), significance=c(0.1, 0.05, 0.01),
lookup=TRUE, n.realization=10000, n.repetition=3,
tolerance=1e-6)a logical flag for accessing precalculated
critical D-statistics. The
critical D-statistics are calculated for a variety of sample sizes
and significances. If lookup is TRUE (recommended), this table is
accessed. The table is stored as the matrix object D.table.critical. Missing table values are calculated
using the input arguments: n.realization, n.repetition, and tolerance. Default: TRUE.
an integer specifying the number of realizations to generate in a
Monte Carlo simulation for calculating the D-statistic(s). This
parameter is used either when lookup is FALSE,
or when lookup is TRUE and the table is missing
values corresponding to the specified significances. Default: 10000.
an integer specifying the number of Monte Carlo simulations to
perform. This parameter coordinates with the n.realization
parameter. Default: 3.
a vector of integers denoting the sample sizes for which critical
D-statistics are created. Default: c(127,130).
a numeric vector of real values in the interval (0,1).
The significance is the fraction of times that the
linear cumulative energy hypothesis is incorrectly rejected. It is
equal to the difference of the distribution probability (p) and unity.
Default: c(0.1, 0.05, 0.01).
a numeric real scalar that specifies the amplitude threshold to use in
estimating critical D-statistic(s) via the Inclan-Tiao approximation.
Setting this parameter to a higher value
results in a lesser number of summation terms at the expense of obtaining
a less accurate approximation. Default: 1e-6.
a matrix containing the critical
D-statistics corresponding to the supplied sample sizes and
significances.
A precalculated critical D-statistics object
(D.table.critical) exists
on the package workspace and was built for a variety of sample sizes and
significances using 3 repetitions and 10000
realizations/repetition. This D.table function should be used in
cases where specific D-statistics are missing from
D.table.critical.
Note: the results of the D.table value should not be returned to a
variable named D.table.critical as it will override the
precalculated table available in the package.
An Inclan-Tiao approximation of critical D-statistics is used for sample
sizes n.sample \(\ge 128\) while a Monte Carlo technique is used for
n.sample \(< 128\). For the
Monte Carlo technique, the D-statistic for a
Gaussian white noise sequence of length n.sample is calculated. This
process is repeated n.realization times, forming a distribution of the
D-statistic. The critical values corresponding to the significances
are calculated a total of n.repetition times, and averaged to form
an approximation to the D-statistic(s).
D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000.
# NOT RUN {
D.lookup <- D.table(significance=c(10,5,1)/100,
n.realization=100, n.sample=125:130, lookup=FALSE)
# }
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