hfit: Perform maximum likelihood estimation

In emhawkes: Exponential Multivariate Hawkes Model

Perform maximum likelihood estimation

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 multivariate 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,
  lambda_component0 = 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,
  lambda_component0 = 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 which 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 counting processes weighted by mark.
lambda_component0	Initial values of lambda component. It must have the same dimensional matrix (n by n) with object.
N0	Initial values of N.
mylogLik	User defined log-likelihood function. mylogLik function should have object argument consistent with object.
reduced	When TRUE, reduced estimation performed.
grad	A Gradient matrix for the likelihood function. For more information, see maxLik.
hess	A Hessian matrix for the likelihood function. For more information, see maxLik.
constraint	Constraint matrices. For more information, see maxLik.
method	A 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.

Value

maxLik object

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, inter_arrival=res$inter_arrival, type=res$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, lambda_component0 = matrix(rep(0.1,4), nrow=2))

fit <- hfit(h1,
            inter_arrival = res$inter_arrival,
            type = res$type,
            mark = res$mark,
            lambda_component0 = matrix(rep(0.1,4), nrow=2))
summary(fit)

# For more information, please see vignettes.

emhawkes documentation built on Feb. 16, 2023, 9:02 p.m.