L0TFinv (version 0.1.0)

L0TFinv.fix: The inverse L0 trend filtering with fixed change points

Description

Fit the input data points to a piecewise constant or piecewise linear trend with a given number of change points.

Usage

L0TFinv.fix(y = y, k = k, q = q, first = 0, last = 1)

Value

An S3 object of type "L0TFinvfix". A list containing the fitted trend results:

sic

Information criterion value with a penalty term of \(2\log(\log(n)) \times \log(n)\)

bic

Information criterion value with a penalty term of \(2 \times \log(n)\)

mse

The mean square error between the fitted trend and the input data

y

The input data points

betak

The fitted \(\hat{\boldsymbol{\beta}}\) coefficients with the number of change points being \(k\)

yk

The fitted trend with the number of change points being \(k\)

Ak

The set of position indicators of the fitted change points with the number of change points being \(k\)

beta.all

A data frame with dimensions \(n \times k\), where each column represents the fitted \(\hat{\boldsymbol{\beta}}\) coefficients corresponding to a given number of change points

y.all

A data frame with dimensions \(n \times k\), where each column represents the fitted estimated trend corresponding to a given number of change points

A.all

A list of length \(k\), where each element corresponds to the set of position indicators of change points under a given number

Arguments

y

The input data points

k

The given number of change points

q

0 or 1. Correspond to a piecewise constant or piecewise linear trend

first

The value ranges from 0 to 1. Represent the minimum percentile point where a change point may occur. If 'first' = 0.01, it means that change points cannot appear in the first 1% of the data points. If 'first' = 0, there is no constraint on the position of the change point.

last

The value ranges from 0 to 1. Represent the maximum percentile point where a change point may occur. If 'last' = 0.99, it means that change points cannot appear in the last 1% of the data points. If 'last' = 1, there is no constraint on the position of the change point.

See Also

L0TFinv.opt

Examples

tau = c(0.1, 0.3, 0.4, 0.7, 0.85)
h = c(-1, 5, 3, 0, -1, 2)
BlocksData <- SimuBlocksInv(n = 350, sigma = 0.2, seed = 50, tau = tau ,h = h)
res <- L0TFinv.fix(y=BlocksData$y, k=5, q=0, first=0.01, last=1)
print(res$Ak)
print(BlocksData$setA)
plot(BlocksData$x, BlocksData$y, xlab="", ylab="")
lines(BlocksData$x, BlocksData$y0, col = "red")
lines(BlocksData$x, res$yk, col = "lightgreen")

tau1 = c(0.1, 0.3, 0.4, 0.7, 0.85)
h1 = c(-1, 5, 3, 0, -1, 2)
a0 = -10
WaveData <- SimuWaveInv(n = 2000, sigma = 0.1, seed = 50, tau = tau1, h = h1, a0 = a0)
res1 <- L0TFinv.fix(y=WaveData$y, k=5, q=1, first=0, last=0.99)
print(res1$Ak)
print(WaveData$setA)
plot(WaveData$x, WaveData$y, xlab="", ylab="")
lines(WaveData$x, WaveData$y0, col = "red")
lines(WaveData$x, res1$yk, col = "lightgreen")