Q.mon: Multivariate forward CUSUM monitoring with finite horizon

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

Multivariate forward CUSUM monitoring with finite horizon

Description

Performs the multivariate forward CUSUM monitoring procedure with linear boundary

Usage

Q.mon(
  formula,
  T,
  m = 10,
  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.
m	The length of the relative monitoring period m > 1; default is m = 10. Horizons larger than m=10 are not implemented.
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	A vector containing the path of the detector statistic from T+1 onwards depending on the specificaton for the alternative hypothesis
boundary	A vector containing the values of the linear boundary function from T+1 onwards
detector.scaled	A vector containing the path of the detector divided by the boundary
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
Q.mon(y~1+x+I(x^2), T)
Q.mon(y~1+x+I(x^2), T, alternative = "greater")
H <- matrix(c(1,0,0), ncol = 1)
Q.mon(y~1+x+I(x^2), T, m=6, H = H)

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