Using the Isolate-Detect methodology, this function estimates the number and locations
of multiple change-points in the noisy, continuous, piecewise-linear input vector x,
with noise that is not normally distributed. It also gives the estimated signal, as well as
the solution path defined in sol_path_cplm (see Details for the relevant
literature reference).
ht_ID_cplm(x, s.ht = 3, q_ht = 300, ht_thr_id = 1.4, ht_th_ic_id = 1.25,
p_thr = 1, p_ic = 3)A numeric vector containing the data in which you would like to find change-points.
A positive integer number with default value equal to 3. It is used to define the way we pre-average the given data sequence. For more information see Details.
A positive integer number with default value equal to 300. If the
length of x is less than or equal to q_ht, then no pre-averaging
will take place.
A positive real number with default value equal to 1.4. It is
used to define the threshold, if the thresholding approach (described in cplm_th)
is to be followed.
A positive real number with default value equal to 1.25. It is
useful only if the model selection based Isolate-Detect method is to be followed
and it is used to define the threshold value that will be used at the first step
(change-point overestimation) of the model selection approach described in
cplm_ic. It is applied to the new data, which are obtained
after we take average values on x.
A positive integer with default value equal to 1. It is used only
when the threshold based approach (described in cplm_th) is to
be followed and it defines the distance between two consecutive end- or start-points
of the right- or left-expanding intervals, respectively.
A positive integer with default value equal to 3. It is used only
when the information criterion based approach (described in cplm_ic) is
to be followed and it defines the distance between two consecutive end- or start-points
of the right- or left-expanding intervals, respectively.
A list with the following components:
cpt |
|
| A vector with the detected change-points. | no_cpt |
| The number of change-points detected. | fit |
| A numeric vector with the estimated continuous piecewise-linear signal. |
Firstly, in this function we call normalise, in order to
create a new data sequence, \(\tilde{x}\), by taking averages of observations in
x. Then, we employ ID_cplm on \(\tilde{x}_q\) to obtain the
change-points, namely \(\tilde{r}_1, \tilde{r}_2, ..., \tilde{r}_{\hat{N}}\) in
increasing order. To obtain the original location of the change-points with,
on average, the highest accuracy we define
$$\hat{r}_k = (\tilde{r}_{k}-1)*\code{s.ht} + \lfloor \code{s.ht}/2 + 0.5 \rfloor, k=1, 2,..., \hat{N}.$$
More details can be found in ``Detecting multiple generalized change-points by
isolating single ones'', Anastasiou and Fryzlewicz (2018), preprint.
ID_cplm and normalise, which are functions that are
used in ht_ID_cplm. In addition, see ht_ID_pcm for the case
of piecewise-constant mean signals.
# NOT RUN {
single.cpt <- c(seq(0, 1999, 1), seq(1998, -1, -1))
single.cpt.student <- single.cpt + rt(4000, df = 5)
cpt.single <- ht_ID_cplm(single.cpt.student)
three.cpt <- c(seq(0, 3998, 2), seq(3996, -2, -2), seq(0,3998,2), seq(3996,-2,-2))
three.cpt.student <- three.cpt + rt(8000, df = 5)
cpt.three <- ht_ID_cplm(three.cpt.student)
# }
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