predict.not: Estimate signal for a 'not' object.

Description

Estimates signal in object$x with change-points at cpt. The type of the signal depends on on the value of contrast that has been passed to not (see details below).

Usage

# S3 method for not
predict(object, cpt, ...)

Value

A vector wit the estimated signal or a two-column matrix with the estimated estimated signal and standard deviation if contrast="pcwsConstMeanVar" was used to construct object.

Arguments

object: An object of class 'not', returned by not.
cpt: An integer vector with locations of the change-points. If missing, the features is called internally to extract the change-points from object.
...: Further parameters that can be passed to predict.not and features.

Details

The data points provided in object$x are assumed to follow $$Y_{t} = f_{t}+\sigma_{t}\varepsilon_{t},$$ for $t=1,\ldots,n$, where $n$ is the number of observations in object$x, the signal $f_{t}$ and the standard deviation $\sigma_{t}$ are non-stochastic with change-points at locations given in cpt and $\varepsilon_{t}$ is a white-noise. Denote by $\tau_{1}, \ldots, \tau_{q}$ the elements in cpt and set $\tau_{0}=0$ and $\tau_{q+1}=T$. Depending on the value of contrast that has been passed to not to construct object, the returned value is calculated as follows.

For contrast="pcwsConstantMean" and contrast="pcwsConstantMeanHT", in each segment $(\tau_{j}+1, \tau_{j+1})$, $f_{t}$ for $t\in(\tau_{j}+1, \tau_{j+1})$ is approximated by the mean of $Y_{t}$ calculated over $t\in(\tau_{j}+1, \tau_{j+1})$.
For contrast="pcwsLinContMean", $f_{t}$ is approximated by the linear spline fit with knots at $\tau_{1}, \ldots, \tau_{q}$ minimising the l2 distance between the fit and the data.
For contrast="pcwsLinMean" in each segment $(\tau_{j}+1, \tau_{j+1})$, the signal $f_{t}$ for $t\in(\tau_{j}+1, \tau_{j+1})$ is approximated by the line $\alpha_{j} + \beta_{j} t$, where the regression coefficients are found using the least squares method.
For contrast="pcwsQuad", the signal $f_{t}$ for $t\in(\tau_{j}+1, \tau_{j+1})$ is approximated by the curve $\alpha_{j} + \beta_{j} t + \gamma_{j} t^2$, where the regression coefficients are found using the least squares method.
For contrast="pcwsConstMeanVar", in each segment $(\tau_{j}+1, \tau_{j+1})$, $f_{t}$ and $\sigma_{t}$ for $t\in(\tau_{j}+1, \tau_{j+1})$ are approximated by, respectively, the mean and the standard deviation of $Y_{t}$, both calculated over $t\in(\tau_{j}+1, \tau_{j+1})$.

Examples

Run this code

# **** Piecewisce-constant mean with Gaussian noise.
x <- c(rep(0, 100), rep(1,100)) + rnorm(100)
# *** identify potential locations of the change-points
w <- not(x, contrast = "pcwsConstMean")
# *** when 'cpt' is omitted, 'features' function is used internally 
# to choose change-points locations
signal.est <- predict(w)
# *** estimate the signal specifying the location of the change-point
signal.est.known.cpt <- predict(w, cpt=100)
# *** pass arguments of the 'features' function through 'predict'.
signal.est.aic <- predict(w, penalty.type="aic")

# **** Piecewisce-constant mean and variance with Gaussian noise.
x <- c(rep(0, 100), rep(1,100)) + c(rep(2, 100), rep(1,100)) * rnorm(100)
# *** identify potential locations of the change-points
w <- not(x, contrast = "pcwsConstMeanVar")
# *** here signal is two-dimensional
signal.est <- predict(w)