Functions for estimating point processes.
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 MPP
plot(x, ...)
# S3 method for PP
plot(x, ...)
# S3 method for sePP
plot(x, ...)
vector
, times at which to calculate
self-excitement function.
timeSeries
object or vector
.
numeric
, indicating Hawkes or ETAS models and
whether marks may have an influence on future points.
character
, name of density of mark
distribution, currently only "GPD".
logical
, whether marks of marked point
process may influence the self-excitement.
vector
, marks associated with point events.
character
, name of self-exciting model.
integer
, count of upper extremes to be used.
list
, a point process object of class PP
or
MPP
.
logical
, whether previous events may
influence the scaling of mark distribution.
list
, a fitted self-exciting process created with
fit.sePP()
or a marked self-exciting process created with
fit.seMPP()
.
logical
, whether standard errors should be
computed.
vector
, parameters of self-excitement function.
numeric
, threshold value.
vector
, times of point events.
list
, a (un/marked) point process object of class
PP
/MPP
.
ellipsis, arguments passed to plot()
or to
fit.GPD()
for fit.POT()
or to nlminb()
for
functions fit.sePP()
and fit.seMPP
or to julian()
for extremalPP
.
The function extremalPP()
returns a list describing class MPP
(marked point process) consisting of times and magnitudes of threshold
exceedances:
vector of julian day counts (since 1/1/1960) for each exceedance
vector of exceedances values (differences between value and threshold at each mark)
the julian count one day prior to the first date in the entire timeSeries
value of last julian count in entire timeSeries
value of threshold above which exceedances are calculated
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.
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()
.
# NOT RUN {
## Extremal PP
library(QRM)
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)
# }
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