Find the first changepoint in the mean using EWMA, assuming prechange known

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Description

Given a vector x, control parameters r and L, and a burn-in length BL, returns a list containing the changepoints. Algorithm is implemented in C++.

Usage

1
cpp_detectEWMAMeanSinglePrechange(x, r, L, prechangeMean, prechangeSigma)

Arguments

x

Vector of numeric values values.

r

control parameter for EWMA. Must be in range [0,1].

L

control parameter for EWMA.

BL

Value for the burn-in length.

Details

EWMA updates via:

Z_{j} = (1-r) Z_{j-1} + r x_{j}

where μ is the mean of the in-control stream, x_j is the observation at time j and r is a control parameter for EWMA. Then, a change is signalled if

|Z_j - μ| > L σ_{Z_j}

, where L is the other control parameter, and σ_{Z_j} is a scaled version of the in-control variance σ. This is the formulation for using EWMA to detect an increase or decrease in the mean.

Value

A list with

tauhat

A vector of the changepoints found.

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