EstimCarmaHawkes {yuima}

Estimation Methods for a CARMA(p,q)-Hawkes Counting Process

Description

The function provides two estimation procedures: Maximum Likelihood Estimation and Matching Empirical Correlation

Usage

EstimCarmaHawkes(yuima, start, est.method = "qmle", method = "BFGS", 
lower = NULL, upper = NULL, lags = NULL, display = FALSE)

Arguments

yuima

a yuima object.

start

initial values to be passed to the optimizer.

est.method

The method used to estimate the parameters. The default est.method = "qmle" indicates the MLE while the alternative approach is based on the minimization of the empirical and theoretical autocorrelation.

method

The optimization method to be used. See optim.

lower

Lower Bounds.

upper

Upper Bounds.

lags

Number of lags used in the autocorrelation.

display

you can see a progress of the estimation when display=TRUE.

Value

The output contains the estimated parameters.

Author(s)

The YUIMA Project Team

Contacts: Lorenzo Mercuri [e-mail]

References

Mercuri, L., Perchiazzo, A., & Rroji, E. (2022). A Hawkes model with CARMA (p, q) intensity. doi:10.48550/arXiv.2208.02659.

Examples

## Not run: 
## MLE For A CARMA(2,1)-Hawkes ##

# Inputs:
a <- c(3,2)
b <- c(1,0.3)
mu<-0.30

true.par<-c(mu,a,b)

# step 1) Model Definition => Constructor 'setCarmaHawkes'
p <- 2
q <- 1
mod1 <- setCarmaHawkes(p = p,q = q)

# step 2) Grid Construction => Constructor 'setSampling'
FinalTime <- 5000
t0 <- 0
samp <- setSampling(t0, FinalTime, n = FinalTime)

# step 3) Simulation => method 'simulate'
# We use method 'simulate' to generate our dataset. 
# For the estimation from real data, 
# we use the constructors 'setData' and 
#'setYuima' (input 'model' is an object of 
#           'yuima.CarmaHawkes-class'). 

names(true.par) <- c(mod1@[e-mail], mod1@[e-mail], mod1@[e-mail]) 

set.seed(1)
system.time(
sim1 <- simulate(object = mod1, true.parameter = true.par, 
    sampling = samp)
)

plot(sim1)

# step 4) Estimation using the likelihood function.
system.time(
  res <- EstimCarmaHawkes(yuima = sim1, 
    start = true.par)
)


## End(Not run)