# est_signal: Estimate the signal In IDetect: Isolate-Detect Methodology for Multiple Change-Point Detection

## Description

This function estimates the signal in a given data sequence x with change-points at cpt. The type of the signal depends on whether the change-points represent changes in a piecewise-constant or continuous, piecewise-linear signal. For more information see Details below.

## Usage

 1 est_signal(x, cpt, type = c("mean", "slope")) 

## Arguments

 x A numeric vector containing the given data. cpt A positive integer vector with the locations of the change-points. If missing, the ID_pcm or the ID_cplm function (depending on the type of the signal) is called internally to extract the change-points in x. type A character string, which defines the type of the detected change-points. If type = mean'', then the change-points represent the locations of changes in the mean of a piecewise-constant signal. If type = slope'', then the change-points represent the locations of changes in the slope of a continuous, piecewise-linear signal.

## Details

The data points provided in x are assumed to follow

X_t = f_t + σε_t; t = 1,2,...,T,

where T is the total length of the data sequence, X_t are the observed data, f_t is a one-dimensional, deterministic signal with abrupt structural changes at certain points, and ε_t is white noise. We denote by r_1, r_2, ..., r_N the elements in cpt and by r_0 = 0 and r_{N+1} = T. Depending on the value that has been passed to type, the returned value is calculated as follows.

• For type = mean'', in each segment (r_j + 1, r_{j+1}), f_t for t \in (r_j + 1, r_{j+1}) is approximated by the mean of X_t calculated over t \in (r_j + 1, r_{j+1}).

• For type = slope'', f_t is approximated by the linear spline fit with knots at r_1, r_2, ..., r_N minimising the l_2 distance between the fit and the data.

## Value

A numeric vector with the estimated signal.

## Author(s)

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

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 single.cpt.pcm <- c(rep(4,1000),rep(0,1000)) single.cpt.pcm.noise <- single.cpt.pcm + rnorm(2000) cpt.single.pcm <- ID_pcm(single.cpt.pcm.noise) fit.cpt.single.pcm <- est_signal(single.cpt.pcm.noise, cpt.single.pcm$cpt, type = "mean") three.cpt.pcm <- c(rep(4,500),rep(0,500),rep(-4,500),rep(1,500)) three.cpt.pcm.noise <- three.cpt.pcm + rnorm(2000) cpt.three.pcm <- ID_pcm(three.cpt.pcm.noise) fit.cpt.three.pcm <- est_signal(three.cpt.pcm.noise, cpt.three.pcm$pcm, type = "mean") single.cpt.plm <- c(seq(0,999,1),seq(998.5,499,-0.5)) single.cpt.plm.noise <- single.cpt.plm + rnorm(2000) cpt.single.plm <- ID_cplm(single.cpt.plm.noise) fit.cpt.single.plm <- est_signal(single.cpt.plm.noise, cpt.single.plm\$cpt, type = "slope") 

IDetect documentation built on May 2, 2019, 11:04 a.m.