hfit: Perform Maximum Likelihood Estimation

In ksublee/emhawkes: Exponential Multivariate Hawkes Model

Perform Maximum Likelihood Estimation

Description

This is a generic function named hfit designed for estimating the parameters of the exponential Hawkes model. It is implemented as an S4 method for two main reasons:

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	An hspec-class object containing the parameter values.
inter_arrival	A vector of inter-arrival times for events across all dimensions, starting with zero.
type	A vector indicating the dimensions, represented by numbers like 1, 2, 3, etc., starting with zero.
mark	A vector of mark (jump) sizes, starting with zero.
N	A matrix representing counting processes.
Nc	A matrix of counting processes weighted by mark sizes.
lambda_component0	Initial values for the lambda component \lambda_{ij}. Can be a numeric value or a matrix. Must have the same number of rows and columns as alpha or beta in object.
N0	Initial values for the counting processes matrix N.
mylogLik	A user-defined log-likelihood function, which must accept an object argument consistent with object.
reduced	Logical; if TRUE, performs reduced estimation.
grad	A gradient matrix for the likelihood function. Refer to maxLik for more details.
hess	A Hessian matrix for the likelihood function. Refer to maxLik for more details.
constraint	Constraint matrices. Refer to maxLik for more details.
method	The optimization method to be used. Refer to maxLik for more details.
verbose	Logical; if TRUE, prints the progress of the estimation process.
...	Additional parameters for optimization. Refer to maxLik for more details.

Details

Model Representation: To represent the structure of the model as an hspec object. The multivariate marked Hawkes model has numerous variations, and using an S4 class allows for a flexible and structured approach.

Optimization Initialization: To provide a starting point for numerical optimization. The parameter values assigned to the hspec slots serve as initial values for the optimization process.

This function utilizes the maxLik package for optimization.

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.

ksublee/emhawkes documentation built on Feb. 5, 2025, 1:35 a.m.