# ht_ID_cplm: Apply the Isolate-Detect methodology for multiple... In IDetect: Isolate-Detect Methodology for Multiple Change-Point Detection

## Description

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).

## Usage

 1 2 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) 

## Arguments

 x A numeric vector containing the data in which you would like to find change-points. s.ht 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. q_ht 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. ht_thr_id 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. ht_th_ic_id 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. p_thr 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. p_ic 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.

## Details

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.

## Value

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. solution_path A vector containing the solution path.

## Author(s)

Andreas Anastasiou, a.anastasiou@lse.ac.uk

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.
 1 2 3 4 5 6 7 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)