residual_process {emhawkes}

Compute residual process

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,
  inter_arrival,
  type,
  rambda_component,
  mu,
  beta,
  dimens = NULL,
  mark = NULL,
  N = NULL,
  Nc = NULL,
  lambda_component0 = NULL,
  N0 = NULL,
  ...
)

Arguments

component

The component of type to get the residual process.

inter_arrival

Inter-arrival times of events. This includes inter-arrival for events that occur in all dimensions. Start with zero.

type

A vector of types distinguished by numbers, 1, 2, 3, and so on. 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 counting processes weighted by mark.

lambda_component0

The initial values of lambda component. Must have the same dimensional matrix with hspec.

N0

The initial value of N

...

Further arguments passed to or from other methods.

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(component = 1, res$inter_arrival, res$type, res$rambda_component, mu, beta)