IDetect (version 0.1.0)

est_signal: Estimate the signal

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

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.

Value

A numeric vector with the estimated signal.

Details

The data points provided in x are assumed to follow $$X_t = f_t + \sigma\epsilon_t; t = 1,2,...,T,$$ 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 \(\epsilon_t\) 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.

Examples

# NOT RUN {
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")
# }