residual_process: Compute residual process

In emhawkes: Exponential Multivariate Hawkes Model

Description

Using random time change, this function compute the residual process, which is the inter-arrival time of a standard Poisson process. Therefore, the return values should follow the exponential distribution with rate 1, if model and rambda are correctly specified.

Usage

residual_process(
  component,
  type,
  inter_arrival,
  rambda_component,
  mu,
  beta,
  dimens = NULL,
  mark = NULL,
  N = NULL,
  Nc = NULL,
  lambda0 = NULL,
  N0 = NULL
)

Arguments

component	the component of type to get the residual process
type	a vector of types. Distinguished by numbers, 1, 2, 3, and so on. Start with zero.
inter_arrival	inter-arrival times of events. Includes inter-arrival for events that occur in all dimensions. Start with zero.
rambda_component	right continuous version of lambda process
mu	numeric value or matrix or function, if numeric, automatically converted to matrix
beta	numeric value or matrix or function, if numeric, automatically converted to matrix, exponential decay
dimens	dimension of the model. if omitted, set to be the length of mu.
mark	a vector of realized mark (jump) sizes. Start with zero.
N	a matrix of counting processes
Nc	a matrix of cumulated counting processes
lambda0	the initial values of lambda component. Must have the same dimensional matrix with hspec.
N0	the initial value of N

Examples

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=1000)
rp <- residual_process(1, res$type, res$inter_arrival, res$rambda_component, mu, beta)
p <- ppoints(100)
q <- quantile(rp,p=p)
plot(qexp(p), q, xlab="Theoretical Quantiles",ylab="Sample Quantiles")
qqline(q, distribution=qexp,col="blue", lty=2)

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