hfit: Perform Maximum Likelihood Estimation

In emhawkes: Exponential Multivariate Hawkes Model

Description

Generic function hfit. A method for estimating the parameters of the exponential Hawkes model. The reason for being constructed as the S4 method is as follows. First, to represent the structure of the model as an hspec object. There are numerous variations on the mutlivariate marked Hawkes model. Second, to convey the starting point of numerical optimization. The parameter values assigned to the hspec slots become initial values. This function uses maxLik for the optimizer.

Usage

hfit(
  object,
  inter_arrival = NULL,
  type = NULL,
  mark = NULL,
  N = NULL,
  Nc = NULL,
  lambda0 = NULL,
  N0 = NULL,
  mylogLik = NULL,
  reduced = TRUE,
  grad = NULL,
  hess = NULL,
  constraint = NULL,
  method = "BFGS",
  verbose = FALSE,
  ...
)

## S4 method for signature 'hspec'
hfit(
  object,
  inter_arrival = NULL,
  type = NULL,
  mark = NULL,
  N = NULL,
  Nc = NULL,
  lambda0 = NULL,
  N0 = NULL,
  mylogLik = NULL,
  reduced = TRUE,
  grad = NULL,
  hess = NULL,
  constraint = NULL,
  method = "BFGS",
  verbose = FALSE,
  ...
)

Arguments

object	hspec-class. This object includes the parameter values
inter_arrival	inter-arrival times of events. Includes inter-arrival for events that occur in all dimensions. Start with zero.
type	a vector of dimensions. Distinguished by numbers, 1, 2, 3, and so on. Start with zero.
mark	a vector of mark (jump) sizes. Start with zero.
N	a matrix of counting processes
Nc	a matrix of cumulated counting processes
lambda0	the inital values of lambda component. Must have the same dimensional matrix (n by n) with hspec.
N0	the initial values of N.
mylogLik	user defined log likelihood function. mylogLik function should have 'object' argument, cosistent with hspec.
reduced	When TRUE, reduced estimation performed.
grad	gradient matrix for the likelihood function. For more information, see maxLik.
hess	Hessian matrix for the likelihood function. For more information, see maxLik.
constraint	constraint matrix. For more information, see maxLik.
method	method for optimization. For more information, see maxLik.
verbose	If TRUE, print the progress of the estimation.
...	other parameters for optimization. For more information, see maxLik.

See Also

hspec-class, hsim,hspec-method

Examples

# example 1
mu <- c(0.1, 0.1)
alpha <- matrix(c(0.2, 0.1, 0.1, 0.2), nrow=2, byrow=TRUE)
beta <- matrix(c(0.9, 0.9, 0.9, 0.9), nrow=2, byrow=TRUE)
h <- new("hspec", mu=mu, alpha=alpha, beta=beta)
res <- hsim(h, size=100)
summary(hfit(h, res$inter_arrival, res$type))


# example 2

mu <- matrix(c(0.08, 0.08, 0.05, 0.05), nrow = 4)
alpha <- function(param = c(alpha11 = 0, alpha12 = 0.4, alpha33 = 0.5, alpha34 = 0.3)){
  matrix(c(param["alpha11"], param["alpha12"], 0, 0,
           param["alpha12"], param["alpha11"], 0, 0,
           0, 0, param["alpha33"], param["alpha34"],
           0, 0, param["alpha34"], param["alpha33"]), nrow = 4, byrow = TRUE)
}
beta <- matrix(c(rep(0.6, 8), rep(1.2, 8)), nrow = 4, byrow = TRUE)

impact <- function(param = c(alpha1n=0, alpha1w=0.2, alpha2n=0.001, alpha2w=0.1),
                   n=n, N=N, ...){

  Psi <- matrix(c(0, 0, param['alpha1w'], param['alpha1n'],
                  0, 0, param['alpha1n'], param['alpha1w'],
                  param['alpha2w'], param['alpha2n'], 0, 0,
                  param['alpha2n'], param['alpha2w'], 0, 0), nrow=4, byrow=TRUE)

  ind <- N[,"N1"][n] - N[,"N2"][n] > N[,"N3"][n] - N[,"N4"][n] + 0.5

  km <- matrix(c(!ind, !ind, !ind, !ind,
                 ind, ind, ind, ind,
                 ind, ind, ind, ind,
                 !ind, !ind, !ind, !ind), nrow = 4, byrow = TRUE)

  km * Psi
}
h <- new("hspec",
         mu = mu, alpha = alpha, beta = beta, impact = impact)
hr <- hsim(h, size=100)
plot(hr$arrival, hr$N[,'N1'] - hr$N[,'N2'], type='s')
lines(hr$N[,'N3'] - hr$N[,'N4'], type='s', col='red')
fit <- hfit(h, hr$inter_arrival, hr$type)
summary(fit)


# example 3

mu <- c(0.15, 0.15)
alpha <- matrix(c(0.75, 0.6, 0.6, 0.75), nrow=2, byrow=TRUE)
beta <- matrix(c(2.6, 2.6, 2.6, 2.6), nrow=2, byrow=TRUE)
rmark <- function(param = c(p=0.65), ...){
  rgeom(1, p=param[1]) + 1
}
impact <- function(param = c(eta1=0.2), alpha, n, mark, ...){
  ma <- matrix(rep(mark[n]-1, 4), nrow = 2)
  alpha * ma * matrix( rep(param["eta1"], 4), nrow=2)
}
h1 <- new("hspec", mu=mu, alpha=alpha, beta=beta,
          rmark = rmark,
          impact=impact)
res <- hsim(h1, size=100, lambda0 = matrix(rep(0.1,4), nrow=2))

fit <- hfit(h1,
            inter_arrival = res$inter_arrival,
            type = res$type,
            mark = res$mark,
            lambda0 = matrix(rep(0.1,4), nrow=2))
summary(fit)

# For more information, please see vignettes.

emhawkes documentation built on Feb. 16, 2021, 9:06 a.m.