hfit | R Documentation |
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:
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,
...
)
object |
An |
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 |
N0 |
Initial values for the counting processes matrix |
mylogLik |
A user-defined log-likelihood function, which must accept an |
reduced |
Logical; if |
grad |
A gradient matrix for the likelihood function. Refer to |
hess |
A Hessian matrix for the likelihood function. Refer to |
constraint |
Constraint matrices. Refer to |
method |
The optimization method to be used. Refer to |
verbose |
Logical; if |
... |
Additional parameters for optimization. Refer to |
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.
maxLik
object
hspec-class
, hsim,hspec-method
# 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.
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