infer_lambda {emhawkes}

Infer lambda process with given Hawkes model and realized path

Description

This method compute the inferred lambda process and returns it as hreal form. If we have realized path of Hawkes process and its parameter value, then we can compute the inferred lambda processes. Similarly with other method such as hfit, the input arguments are inter_arrival, type, mark, or equivalently, N and Nc.

Usage

infer_lambda(
  object,
  inter_arrival = NULL,
  type = NULL,
  mark = NULL,
  N = NULL,
  Nc = NULL,
  lambda_component0 = NULL,
  N0 = NULL,
  ...
)

## S4 method for signature 'hspec'
infer_lambda(
  object,
  inter_arrival = NULL,
  type = NULL,
  mark = NULL,
  N = NULL,
  Nc = NULL,
  lambda_component0 = NULL,
  N0 = NULL,
  ...
)

Arguments

object

hspec-class. This object includes the parameter values.

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 dimensions. Distinguished by numbers, 1, 2, 3, and so on. Start with zero.

mark

a vector of mark (jump) sizes. Start with zero.

N

Hawkes process. If not provided, then generate using inter_arrival and type.

Nc

mark accumulated Hawkes process. If not provided, then generate using inter_arrival, type and mark.

lambda_component0

the initial values of lambda component. Must have the same dimensional matrix (n by n) with hspec.

N0

the initial values of N.

...

further arguments passed to or from other methods.

Value

hreal S3-object, with inferred intensity.

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=100)
summary(res)
res2 <- infer_lambda(h, res$inter_arrival, res$type)
summary(res2)