Point Processes

Description

Functions for estimating point processes.

Usage

extremalPP(data, threshold = NA, nextremes = NA, ...)
unmark(PP)
fit.POT(PP, markdens = "GPD", ...)
fit.sePP(PP, model = c("Hawkes", "ETAS"), mark.influence = TRUE,
         std.errs = FALSE, ...)
fit.seMPP(PP, markdens = "GPD", model = c("Hawkes", "ETAS"),
          mark.influence = TRUE, predictable = FALSE,
          std.errs = FALSE, ...)
stationary.sePP(sePP)
sePP.negloglik(theta, PP, case)
seMPP.negloglik(theta, PP, case, markdens)
volfunction(anytimes, times, marks, theta, model)
## S3 method for class 'MPP'
plot(x, ...)
## S3 method for class 'PP'
plot(x, ...)
## S3 method for class 'sePP'
plot(x, ...)

Arguments

Details

extremalPP(): returns a list describing a marked point process (see pages 298-301 of QRM).
fit.POT(): fits the POT (peaks-over-threshold) model to a point process of class PP or MPP. Note that if point process is of class PP, then function simply esitmates the rate of a homogeneous Poisson process (see pages 301–305 of QRM).
fit.seMPP(): fits a marked self-exciting process to a point process object of class MPP.
fit.sePP(): fits self-exciting process to a point process object of class PP (unmarked) or MPP (marked).
seMPP.negloglik(): evaluates negative log-likelihood of a marked self-exciting point process model; this objective function will be passed to the optimizing function.
sePP.negloglik(): evaluates negative log-likelihood of a self-exciting point process model (unmarked).
stationary.sePP(): checks a sufficient condition for stationarity of a self-exciting model and gives information about cluster size.
unmark(): strips marks from a marked point process.
volfunction(): calculates a self-excitement function for use in the negloglik methods used in fit.sePP() and fit.seMPP().

Value

The function extremalPP() returns a list describing class MPP (marked point process) consisting of times and magnitudes of threshold exceedances:

The functions fit.POT(), fit.seMPP(), and fit.sePP() return a list containing the fitted model.

The plot-methods return invisibly the data for producing these.

See Also

GPD, nlminb

Examples

## Extremal PP
data(sp500)
l <- -returns(sp500) 
lw <- window(l, start = "1995-12-31", end = end(l)) 
mod1 <- extremalPP(lw, ne = 100) 
mod1$marks[1:5]
mod1$threshold
mod2a <- fit.sePP(mod1, mark.influence = FALSE, std.errs = TRUE)
mod2b <- fit.seMPP(mod1, mark.influence = FALSE, std.errs = TRUE)
stationary.sePP(mod2b)
mod2c <- fit.POT(mod1, method = "BFGS")
plot(mod1)
plot(unmark(mod1))
plot(mod2a)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(QRM)
Loading required package: gsl
Loading required package: Matrix
Loading required package: mvtnorm
Loading required package: numDeriv
Loading required package: timeSeries
Loading required package: timeDate

Attaching package: 'QRM'

The following object is masked from 'package:base':

    lbeta

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/QRM/PointProcess.Rd_%03d_medium.png", width=480, height=480)
> ### Name: PointProcess
> ### Title: Point Processes
> ### Aliases: PointProcess extremalPP unmark fit.POT fit.sePP fit.seMPP
> ###   stationary.sePP plot.MPP plot.PP plot.sePP sePP.negloglik
> ###   seMPP.negloglik volfunction SEprocExciteFunc
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Extremal PP
> data(sp500)
> l <- -returns(sp500) 
> lw <- window(l, start = "1995-12-31", end = end(l)) 
> mod1 <- extremalPP(lw, ne = 100) 
> mod1$marks[1:5]
[1] 0.011492882 0.002680738 0.005872111 0.001429676 0.002075903
> mod1$threshold
[1] 0.01981916
> mod2a <- fit.sePP(mod1, mark.influence = FALSE, std.errs = TRUE)
> mod2b <- fit.seMPP(mod1, mark.influence = FALSE, std.errs = TRUE)
> stationary.sePP(mod2b)
  stationary          eta cluster.size 
   1.0000000    0.6549983    2.8985365 
> mod2c <- fit.POT(mod1, method = "BFGS")
> plot(mod1)
> plot(unmark(mod1))
> plot(mod2a)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>