Given a vector x, control parameters k and h,
and a burn-in length BL, returns a list containing the changepoints.
Algorithm is implemented in 'C++'.
cpp_detectCUSUMMeanSinglePrechange(x, k, h, prechangeMean, prechangeSigma)A list with
tauhatA vector of the changepoints found.
Vector of numeric values values.
control parameter for CUSUM
control parameter for CUSUM
Value for the burn-in length.
'CUSUM' updates via: $$S_{j} = \max{0, S_{j-1} + (x_{j} - \mu)/ \sigma - k}$$ where \(\mu\) and \(\sigma\) are, respectively, the mean and variance of the in-control stream, \(x_j\) is the observation at time \(j\) and \(k\) is a control parameter for CUSUM. Then, a change is signalled if \(S_j > h\), where \(h\) is the other control parameter. This is the formulation for using 'CUSUM' to detect an increase in the mean; there is a similar formulation for detecting a decrease, and usually 'CUSUM' is two-sided (monitors for an increase and a decrease in the mean).