HDCD (version 1.0)

single_CUSUM: CUSUM transformation of matrix at a specific position

Description

R wrapper for C function computing the CUSUM transformation of matrix over an interval \((s,e]\) evaluated at a specific position. For compatibility with C indexing, the user should subtract \(1\) from \(s\), \(e\) and \(v\) when supplying the arguments to the function. If start and stop are not supplied, the CUSUM is computed over the full data, so \((s,e] = (0,n]\).

Usage

single_CUSUM(X, start = NULL, stop = NULL, pos)

Value

A vector of CUSUM values, each corresponding to a row of the input matrix. The \(i\)-th element corresponds to the CUSUM transformation of the \(i\)-th row of \(X\), computed over the interval \((\code{start}+1,\code{end}+1]\) and evaluated at position \(\code{pos}\), i.e. \(\sqrt{\frac{e-v}{(e-s)(v-s)}}\sum_{t=s+1}^v X_{i,t} - \sqrt{\frac{v-s}{(e-s)(e-v)}}\sum_{t=v+1}^e X_{i,t}\), where \(s = (\code{start}+1)\), \(e = (\code{stop}+1)\) and \(v = \code{pos}+1\).

Arguments

X

Matrix of observations, where each row contains a time series

start

Starting point of interval over which the CUSUM should be computed, subtracted by one

stop

Ending point of interval over which the CUSUM should be computed, subtracted by one

pos

Position at which the CUSUM should be evaluated, subtracted by one

Examples

n = 10
p = 10
set.seed(101)
X = matrix(rnorm(n*p), ncol = n, nrow=p)
# CUSUM over the full data (s,e] = (0,n] evaluated at position v=4
position = 4
X_cusum_single = single_CUSUM(X,pos = position-1)
X_cusum_single

# verifying that this corresponds to the 4-th row of output of CUSUM():
X_cusum = CUSUM(X)
X_cusum[,4]