processStream: Detects Multiple Change Points in a Sequence

Description

This function is used to detect a multiple change points in a sequence of observations using the Change Point Model (CPM) framework for sequential (Phase II) change detection. The observations are processed in order, starting with the first, and a decision is made after each observation whether a change point has occurred. A full description of the CPM framework can be found in the papers cited in the reference section. Unlike the detectChange function, processStream does not terminate and return when a change point is encountered. Instead, a new CPM is initialised immediately following the change point, with all previous observations being discarded. The monitoring then continues, starting from the first observation after the change point. If more change points are discovered later in the sequence, the CPM is again reinitialised after each one. In this way, the whole sequence of observations will be processed and multiple change points may be detected. For a fuller overview of this function including a description of the CPM framework and examples of how to use the various functions, please consult the package manual "Parametric and Nonparametric Sequential Change Detection in R: The cpm Package" available from www.gordonjross.co.uk

Usage

processStream(x, cpmType, ARL0=500, startup=20, lambda=NA)

Arguments

Value

xThe sequence of observations which was processed.detectionTimesA vector containing the points in the sequence at which changes were detected, defined as the first observation after which $D_t$ exceeded the test threshold.changePointsA vector containing the best estimates of the change point locations, for each detecting change point. If a change is detected after the $t^{th}$ observation, then the change estimate is the value of $k$ which maximises $D_{k,t}$.

References

Hawkins, D. , Zamba, K. (2005) -- A Change-Point Model for a Shift in Variance, Journal of Quality Technology, 37, 21-31

Hawkins, D. , Zamba, K. (2005b) -- Statistical Process Control for Shifts in Mean or Variance Using a Changepoint Formulation, Technometrics, 47(2), 164-173 Hawkins, D., Qiu, P., Kang, C. (2003) -- The Changepoint Model for Statistical Process Control, Journal of Quality Technology, 35, 355-366. Ross, G. J., Tasoulis, D. K., Adams, N. M. (2011) -- A Nonparametric Change-Point Model for Streaming Data, Technometrics, 53(4) Ross, G. J., Adams, N. M. (2012) -- Two Nonparametric Control Charts for Detecting Arbitary Distribution Changes, Journal of Quality Technology, 44:102-116 Ross, G. J., Adams, N. M. (2013) -- Sequential Monitoring of a Proportion, Computational Statistics, 28(2)

Ross, G. J., (2014) -- Sequential Change Detection in the Presence of Unknown Parameters, Statistics and Computing 24:1017-1030 Ross, G. J., (2015) -- Parametric and Nonparametric Sequential Change Detection in R: The cpm Package, Journal of Statistical Software, forthcoming

Examples

Run this code

## Use a Student-t CPM to detect several mean shift in a stream of 
     ## Gaussian random variables
     x <- c(rnorm(100,0,1),rnorm(100,1,1), rnorm(100,0,1), rnorm(100,-1,1))
     result <- processStream(x,"Student",ARL0=500,startup=20)
     plot(x)
     for (i in 1:length(result$changePoints)) {
         abline(v=result$changePoints[i], lty=2)
     }

     ## Use a Mood CPM to detect several scale shifts in a stream of 
     ##Student-t random variables
     x <- c(rt(100,3),rt(100,3)*2, rt(100,3), rt(100,3)*2)
     result <- processStream(x,"Mood",ARL0=500,startup=20)
     plot(x)
     for (i in 1:length(result$changePoints)) {
         abline(v=result$changePoints[i], lty=2)
     }
     
     ## Use a FET CPM to detect several parameter shifts in a stream of 
     ## Bernoulli observations. In this case, the lambda parameter acts to 
     ## reduce the discreteness of the test statistic.
     x <- c(rbinom(300,1,0.1),rbinom(300,1,0.4), rbinom(300,1,0.7))
     result <- processStream(x,"FET",ARL0=500,startup=20,lambda=0.3)
     plot(x)
     for (i in 1:length(result$changePoints)) {
         abline(v=result$changePoints[i], lty=2)
     }