Description Usage Arguments Value Author(s) References See Also Examples

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

1 2 3 4 5 6 7 8 | ```
MFT.variance(Phi, rcp = NULL, autoset.d_H = TRUE, S = NULL, E = NULL,
d = NULL, H = NULL, alpha = 0.05, sim = 10000,
method = "asymptotic", Q = NA, perform.CPD = TRUE, plot.CPD = TRUE,
plot.var = TRUE, print.output = TRUE, col = NULL,
ylab1 = expression(abs(G[list(h, t)])),
ylab2 = expression(widehat(sigma)^2), cex.legend = 1.2,
cex.diamonds = 1.4, wid = NULL, main = TRUE, plot.Q = TRUE,
plot.M = TRUE, plot.h = TRUE)
``` |

`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 |

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

`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 automatically (Q) |

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

`perform.CPD` |
logical, if TRUE change point detection algorithm is performed |

`plot.CPD` |
logical, if TRUE CPD-scenario is plotted. Only active if perform.CPD == TRUE |

`plot.var` |
logical, should the variance histogram be plotted? Only possible, if plot.CPD=TRUE |

`print.output` |
logical, if TRUE results are printed to the console |

`col` |
"gray" or vector of colors of length(H). Colors for (R_ht) plot, default: NULL -> rainbow colors from blue to red. |

`ylab1` |
character, ylab for 1. graphic |

`ylab2` |
character, ylab for 2. graphic |

`cex.legend` |
numeric, size of annotations in plot |

`cex.diamonds` |
numeric, size of diamonds that indicate change points |

`wid` |
integer,>0, width of bars in variance histogram |

`main` |
logical, indicates if title and subtitle are plotted |

`plot.Q` |
logical, indicates if rejection threshold Q is plotted |

`plot.M` |
logical, indicates if test statistic M is plotted |

`plot.h` |
logical, indicates if a legend for the window set H is plotted |

invisible

`M` |
test statistic |

`varQ` |
rejection threshold |

`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 |

`H` |
window set |

`d` |
step size delta at which processes were evaluated |

`alpha` |
significance level |

Michael Messer, Stefan Albert, Solveig Plomer and Gaby Schneider

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>

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
# 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.variance(Phi,rcp=rcp) # MFT for the variances
``` |

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