Examples: qmle CARMA – fixed parameters

Here we show how to use the argument fixed in the R function qmle for the estimation of a CARMA(p,q) model.

Reference: Iacus, Stefano M., and Lorenzo Mercuri. “Implementation of Lévy CARMA model in Yuima package.”Computational Statistics 30.4 (2015): 1111-1141.

# yuima(>= 1.6.6)
# Brownian-CARMA
carma <- setCarma(p = 2, q = 1)

param <- list(a1 = 4, a2 = 4.75, b0 = 1, b1 = 0.23)

samp <- setSampling(Terminal = 400, n = 1600)

set.seed(123)

simCarma <- simulate(carma, true.parameter = param, sampling = samp)

est <- qmle(simCarma, start = param, fixed = list(b0=1,a2=3))

# CP-CARMA

carmaL <- setCarma(p = 2, q = 1, measure=list(intensity="lamb",df=list("dnorm(z, mu, sig)")), measure.type="CP")

paramL <- list(a1 = 4, a2 = 4.75, b0 = 1, b1 = 0.23, lamb=1, sig = 1, mu=0)

sampL <- setSampling(Terminal = 400, n = 1600)

set.seed(123)

simCarmaL <- simulate(carmaL, true.parameter = paramL, sampling = sampL)

estL <- qmle(simCarmaL, start = paramL, fixed = list(lamb=1.2), Est.Incr = "IncrPar")


summary(estL)