SBQ.mon.infinite: Stacked backward CUSUM monitoring with infinite horizon

In ottosven/backCUSUM: Backward CUSUM for Testing and Monitoring Structural Change

Stacked backward CUSUM monitoring with infinite horizon

Description

Performs the infinite horizon multivariate stacked backward CUSUM monitoring procedure with linear boundary

Usage

SBQ.mon.infinite(
  formula,
  T,
  alternative = c("two.sided", "greater", "less"),
  H = NULL
)

Arguments

formula	Specification of the linear regression model by an object of the class "formula"
T	Length of the training sample. Monitoring starts at T+1.
alternative	A character string specifying the alternative hypothesis; must be one of "two.sided" (default), "greater" or "less". The output detector is the maximum norm of Q_t ("two.sided"), the maximum entry of Q_t ("greater"), or maximum entry of -Q_t ("less"), respectively.
H	An optional matrix for the partial hypothesis H'β_t = H'β_0, where H'Q_t is considered instead of Q_t. H must have orthonormal columns. For a test for a break in the intercept, H can also set to the string "intercept". The full structural break test is considered as the default setting (NULL).

Value

A list containing the following components:

detector.scaled	A vector containing the path of the detector statistic scaled by the boundary function from T+1 onwards depending on the specificaton for the alternative hypothesis
detector.array	A matrix containing the triangular array of the stacked backward cusum detector from T+1 onwards
boundary	A matrix containing the values of the triangular boundary surface from T+1 onwards
statistic	The test statistic; maximum of detector.scaled
detectontime	The vector containing the detection time points for different significance levels, which are the time indices of the first boundary crossing; NA if the null hypothesis is not rejected
alternative	The specification for the alternative hypothesis
critical.value	A vector containing critical values for different significance levels; NA if critical value for this specification is not implemented
rejection	A logical vector containing the test decision for different significance levels; TRUE for rejection; NA if critical value is not implemented

Examples

T <- 100
t <- 5*T
u <- rnorm(t,0,1)
x <- rnorm(t,1,2)
y <- c(rep(0,480), rep(5,20)) + x + I(x^2) + u
SBQ.mon.infinite(y~1+x+I(x^2), T)
SBQ.mon.infinite(y~1+x+I(x^2), T, alternative = "greater")
H <- matrix(c(1,0,0), ncol = 1)
SBQ.mon.infinite(y~1+x+I(x^2), T, H = H)

ottosven/backCUSUM documentation built on April 12, 2022, 10:59 p.m.