This function computes the Darling-Erd<U+00F6>s statistic.
stat_de(dat, a = log, b = log, estimate = FALSE,
use_kernel_var = FALSE, custom_var = NULL, kernel = "ba",
bandwidth = "and", get_all_vals = FALSE)
The data vector
The function that will be composed with \(l(x) = (2 \log x)^{1/2}\)
The function that will be composed with \(u(x) = 2 \log x + \frac{1}{2} \log \log x - \frac{1}{2} \log \pi\)
Set to TRUE
to return the estimated location of the
change point
Set to TRUE
to use kernel methods for long-run
variance estimation (typically used when the data is
believed to be correlated); if FALSE
, then the
long-run variance is estimated using
\(\hat{\sigma}^2_{T,t} = T^{-1}\left(
\sum_{s = 1}^t \left(X_s - \bar{X}_t\right)^2 +
\sum_{s = t + 1}^{T}\left(X_s -
\tilde{X}_{T - t}\right)^2\right)\), where
\(\bar{X}_t = t^{-1}\sum_{s = 1}^t X_s\) and
\(\tilde{X}_{T - t} = (T - t)^{-1}
\sum_{s = t + 1}^{T} X_s\)
Can be a vector the same length as dat
consisting of
variance-like numbers at each potential change point (so
each entry of the vector would be the "best estimate" of
the long-run variance if that location were where the
change point occured) or a function taking two parameters
x
and k
that can be used to generate this
vector, with x
representing the data vector and
k
the position of a potential change point; if
NULL
, this argument is ignored
If character, the identifier of the kernel function as used in
cointReg (see getLongRunVar
); if
function, the kernel function to be used for long-run variance
estimation (default is the Bartlett kernel in cointReg)
If character, the identifier for how to compute the
bandwidth as defined in cointReg (see
getBandwidth
); if function, a function
to use for computing the bandwidth; if numeric, the bandwidth
value to use (the default is to use Andrews' method, as used in
cointReg)
If TRUE
, return all values for the statistic at
every tested point in the data set
If both estimate
and get_all_vals
are FALSE
, the
value of the test statistic; otherwise, a list that contains the test
statistic and the other values requested (if both are TRUE
,
the test statistic is in the first position and the estimated changg
point in the second)
If \(\bar{A}_T(\tau, t_T)\) is the weighted and trimmed CUSUM statistic
with weighting parameter \(\tau\) and trimming parameter \(t_T\) (see
stat_Vn
), then the Darling-Erd<U+00F6>s statistic is
$$l(a_T) \bar{A}_T(1/2, 1) - u(b_T)$$
with \(l(x) = \sqrt{2 \log x}\) and \(u(x) = 2 \log x + \frac{1}{2} \log
\log x - \frac{1}{2} \log \pi\) (\(\log x\) is the natural logarithm of
\(x\)). The parameter a
corresponds to \(a_T\) and b
to
\(b_T\); these are both log
by default.
See horvathricemiller19CPAT to learn more.
# NOT RUN {
CPAT:::stat_de(rnorm(1000))
CPAT:::stat_de(rnorm(1000), use_kernel_var = TRUE, bandwidth = "nw", kernel = "bo")
# }
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