RHawkes (version 1.0)

EM1partial: Partial EM algorithm for the RHawkes process, version 1

Description

Calculates the RHawkes model parameters via a partial Expectation-Maximization (EM1) algorithm of Wheatley, Filimonov and Sornette (2016).

Usage

EM1partial(tms, cens, pars, maxiter = 1000, tol = 1e-8,
         h.fn = function(x, p) dexp(x, rate = 1 / p),
         mu.fn = function(x, p){
              exp(dweibull(x, shape = p[1], scale = p[2], log = TRUE) -
              pweibull(x, shape = p[1], scale = p[2], lower.tail = FALSE, log.p = TRUE))
         },
         H.fn = function(x, p) pexp(x, rate = 1 / p),
         logg.fn = function(x, p){
              dweibull(x, shape = p[1], scale = p[2], log = TRUE) -
              pweibull(x, shape = p[1], scale = p[2], lower.tail = FALSE, log.p = TRUE) 
              - (x / p[2])^p[1]},
         Mu.fn = function(x, p){
              - pweibull(x, shape = p[1], scale = p[2], lower.tail = FALSE, log.p = TRUE)
         })

Arguments

tms

A numeric vector, with values sorted in ascending order. Event times to fit the RHawkes point process model.

cens

A scalar. The censoring time.

pars

A numeric vector containing the parameters of the model, in order of the immigration parameters \(\mu(.)\), offspring parameters \(h(.)\) and lastly the branching ratio \(\eta(.)\).

maxiter

The maximum number of iterations to perform.

tol

The algorithm stops when the difference between the previous iteration and current iteration parameters sum is less than tol.

h.fn

A (vectorized) function. The offspring density function.

mu.fn

A (vectorized) function. The immigration hazard function.

H.fn

A (vectorized) function. Its value at t gives the integral of the offspring density function from 0 to t.

Mu.fn

A (vectorized) function. Its value at t gives the integral of the immigrant hazard function from 0 to t.

logg.fn

A (vectorized) function. The log of the immigrant distribution function.

Value

iterations

The number of iterations until convergence

diff

The absolute sum of the difference between the final two parameter estimates

pars

The parameter estimates from the EM algorithm

Examples

# NOT RUN {
## simulated data
tms <- sort(runif(100,0,100))
## the slower version of the EM algorithms on simulated data with default 
## immigrant hazard function
## and offspring density
system.time( est1 <- EM1partial(tms, 101, c(2,1,0.5,1)) )
# }