# residual_process: Compute residual process In ksublee/emhawkes: Exponential Multivariate Hawkes Model

 residual_process R Documentation

## 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,
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)

```

ksublee/emhawkes documentation built on May 6, 2022, 12:10 p.m.