detectCUSUMMean: Detect a change/changes in a vector using 'CUSUM' method

Description

Given a vector x, use the 'CUSUM' method to sequentially detect changes (or a single change) in the MEAN of the vector.

Usage

detectCUSUMMean(
  x,
  k = 0.25,
  h = 8,
  BL = 50,
  multiple = TRUE,
  single = !multiple,
  usePrechange = FALSE,
  prechangeMean = NULL,
  prechangeSigma = NULL,
  prechangeVar = NULL,
  skipCheck = FALSE
)

Value

A list with the following elements:

tauhat: A vector of the changepoints found.

Arguments

x: The vector (stream) in which to detect change(s).
k: control parameter for 'CUSUM'. Default is 0.25.
h: control parameter for 'CUSUM'. Defqult is 8.00.
BL: The burn-in length. Default is BL=50.
multiple: Boolean to use to decide whether to detect multiple changes or only a single change. Default is TRUE (i.e. detect multiple changes).
single: Boolean to use to decide whether to detect only a single change or multiple changes. Set to !multiple, i.e. default is FALSE. If both single and multiple are set to TRUE, then only a single change will be detected; if both set to FALSE then multiple changes will be detected (i.e. single dominates).
usePrechange: Boolean indicating whether prechange parameters (mean and variance) are known and will be used (or not). Default is FALSE. If TRUE, then prechange mean and standard deviation variance must be specified. See parameters prechangeMean, prechangeSigma and prechangeVar.
prechangeMean: Value to be used for the prechange mean. Default is NULL. If prechangeKnown = TRUE and value is NULL, this will result in an error.
prechangeSigma: Value to be used for the prechange standard deviation. Default is NULL. If prechangeKnown = TRUE and value is NULL, this will result in an error, unless prechangeVar is not NULL.
prechangeVar: Value to be used for the prechange variance. Default is NULL. If prechangeKnown = TRUE and value is NULL, this will result in an error, unless prechangeSigma is not NULL. prechangeVar is set to sqrt(prechangeSigma).
skipCheck: A boolean which allows the function to skip the check of the stream. Default is FALSE.

Author

Dean Bodenham

Details

'CUSUM' updates via: $S_{j} = max 0, S_{j - 1} + (x_{j} - μ) / σ - k$ and $T_{j} = max 0, S_{j - 1} - (x_{j} - μ) / σ - k$ where $μ$ and $σ$ 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 $S_{j} > h$ or $T_{j} > h$ , where $h$ is the other control parameter. This is the formulation for using 'CUSUM' to detect an increase or decrease in the mean.

References

E. S. Page (1954) Continuous inspection schemes. Biometrika, 41(1/2), 100-115

Examples

Run this code

# create a stream with three changepoints
set.seed(8)
x <- rnorm(400, 5, 1) + rep(c(0:3), each=100) # mean is 5 and s.d. is 1

# multiple changepoints
list_cusum <- detectCUSUMMean(x, k=0.25, h=8.00, BL=50, multiple=TRUE)

# now only a single (the first) changepoint
list_cusum2 <- detectCUSUMMean(x, k=0.25, h=8.00, BL=50, single=TRUE)

# now only a single (the first) changepoint, but with the prechange 
# mean and variance known
list_cusum3 <- detectCUSUMMean(x, k=0.25, h=8.00, BL=50, single=TRUE,
                               prechangeMean=5, prechangeSigma=1)

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