changepoints (version 1.1.0)

DP.VAR1: Dynamic programming for VAR1 change points detection through \(l_0\) penalty.

Description

Perform dynamic programming for VAR1 change points detection through \(l_0\) penalty.

Usage

DP.VAR1(X_futu, X_curr, gamma, lambda, delta, eps = 0.001)

Value

An object of class "DP", which is a list with the following structure:

partition

A vector of the best partition.

cpt

A vector of change points estimation.

Arguments

X_futu

A numeric matrix of time series at one step ahead, with horizontal axis being time.

X_curr

A numeric matrix of time series at current step, with horizontal axis being time.

gamma

A numeric scalar of the tuning parameter associated with \(l_0\) penalty.

lambda

A numeric scalar of the tuning parameter for lasso penalty.

delta

A strictly integer scalar of minimum spacing.

eps

A numeric scalar of precision level for convergence of lasso.

Author

Daren Wang & Haotian Xu

References

Wang, Yu, Rinaldo and Willett (2019) <arxiv:1909.06359>

Examples

p = 10
sigma = 1
n = 20
v1 = 2*(seq(1,p,1)%%2) - 1
v2 = -v1
AA = matrix(0, nrow = p, ncol = p-2)
A1 = cbind(v1,v2,AA)*0.1
A2 = cbind(v2,v1,AA)*0.1
A3 = A1
data = simu.VAR1(sigma, p, 2*n+1, A1)
data = cbind(data, simu.VAR1(sigma, p, 2*n, A2, vzero=c(data[,ncol(data)])))
data = cbind(data, simu.VAR1(sigma, p, 2*n, A3, vzero=c(data[,ncol(data)])))
N = ncol(data)
X_curr = data[,1:(N-1)]
X_futu = data[,2:N]
DP_result = DP.VAR1(X_futu, X_curr, gamma = 1, lambda = 1, delta = 5)
DP_result$cpt