MFT.variance {MFT}

MFT.variance

Description

The multiple filter test for variance change detection in point processes on the line.

Usage

MFT.variance(Phi, rcp = NULL, autoset.d_H = TRUE, S = NULL,
  E = NULL, d = NULL, H = NULL, alpha = 0.05,
  method = "asymptotic", sim = 10000, Q = NA, perform.CPD = TRUE,
  print.output = TRUE)

Arguments

Phi

numeric vector of increasing events, input point process

rcp

vector, rate CPs of Phi (if MFT for the rates is used: as CP[,1]), default: constant rate

autoset.d_H

logical, automatic choice of window size H and step size d

S

numeric, start of time interval, default: Smallest multiple of d that lies beyond min(Phi)

E

numeric, end of time interval, default: Smallest multiple of d that lies beyond max(Phi), needs E > S

d

numeric, > 0, step size delta at which processes are evaluated. d is automatically set if autoset.d_H = TRUE

H

vector, window set H, all elements must be increasing ordered multiples of d, the smallest element must be >= d and the largest =< (T/2). H is automatically set if autoset.d_H = TRUE

alpha

numeric, in (0,1), significance level

method

either "asymptotic", or "fixed", defines how threshold Q is derived, default: "asymptotic". If "asymptotic": Q is derived by simulation of limit process L (Brownian motion); possible set number of simulations (sim). If "fixed": Q may be set manually (Q)

sim

integer, > 0, No of simulations of limit process (for approximation of Q), default = 10000

Q

numeric, rejection threshold, default: Q is simulated according to sim and alpha

perform.CPD

logical, if TRUE change point detection algorithm is performed

print.output

logical, if TRUE results are printed to the console

Value

invisible

M

test statistic

varQ

rejection threshold

method

how threshold Q was derived, see 'Arguments' for detailed description

sim

number of simulations of the limit process (approximation of Q)

CP

set of change points estmated by the multiple filter algorithm, increasingly ordered in time

var

estimated variances between adjacent change points

S

start of time interval

E

end of time interval

Tt

length of time interval

H

window set

d

step size delta at which processes were evaluated

alpha

significance level

perform.CPD

logical, if TRUE change point detection algorithm was performed

tech.var

list of technical variables with processes Phi and G_ht

type

type of MFT which was performed: "variance"

Author(s)

Michael Messer, Stefan Albert, Solveig Plomer and Gaby Schneider

References

Stefan Albert, Michael Messer, Julia Schiemann, Jochen Roeper and Gaby Schneider (2017) Multi-scale detection of variance changes in renewal processes in the presence of rate change points. Journal of Time Series Analysis, <doi:10.1111/jtsa.12254>

See Also

MFT.rate, plot.MFT, summary.MFT, MFT.mean, MFT.peaks

Examples

# Rate and variance change detection in Gamma process 
# (rate CPs at t=30 and 37.5, variance CPs at t=37.5 and 52.5) 
set.seed(51)
mu <- 0.03; sigma <- 0.01
p1 <- mu^2/sigma^2; lambda1 <- mu/sigma^2
p2 <- (mu*0.5)^2/sigma^2; lambda2 <- (mu*0.5)/sigma^2
p3 <- mu^2/(sigma*1.5)^2; lambda3 <- mu/(sigma*1.5)^2
p4 <- mu^2/(sigma*0.5)^2; lambda4 <- mu/(sigma*0.5)^2
Phi <- cumsum(c(rgamma(1000,p1,lambda1),rgamma(500,p2,lambda2),
rgamma(500,p3,lambda3),rgamma(300,p4,lambda4)))
# rcp  <- MFT.rate(Phi)$CP[,1] # MFT for the rates
rcp <- c(30,37.5) # but here we assume known rate CPs
mft <- MFT.variance(Phi,rcp=rcp) # MFT for the variances
plot(mft)