R fGarch: presample matrix for garchSpec() - r

Question

I am trying to specify GARCH model by function fGarch::garchSpec() and i need a specified presample. As defined in manual:
presample: a numeric three column matrix with start values for the
series, for the innovations, and for the conditional
variances.
But i am pretty sure, that this is not the correct order. After reading the manuals and codes for functions: 'garchFit', 'garchSpec', 'garchSim' I am still quite confused.
The question is: how to exactly build presample matrix?

Answer 1

You don't need to set an argument to presample. It will supply a "good" guess and in estimating the parameters it will not matter. If you want to simulate data, then I would just make sure the burnin, n.start, is large enough.
Let's look at an example:
library(fGarch)
## First we simulate some data without setting presample:
# we set up the model by spec:
set.seed(911)
spec <- garchSpec(model = list(mu = 0.02, omega = 0.05, alpha = 0.2, beta = 0.75))
# then simulate our GARCH(1,1) model:
garchSim <- garchSim(spec, n = 200, n.start = 1)
plot(garchSim)
And estimates:
> garchFit(~ garch(1, 1), data = garchSim)
Error Analysis:
Estimate Std. Error t value Pr(>|t|)
mu -0.02196 0.05800 -0.379 0.7049
omega 0.03567 0.02681 1.331 0.1833
alpha1 0.12074 0.04952 2.438 0.0148 *
beta1 0.84527 0.05597 15.103 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Log Likelihood:
-265.8417 normalized: -1.329209
Let us now try to add a very xtreme presample. In the above model (and this seed) the presample was:
> spec#presample
Presample:
time z h y
1 0 -0.4324072 1 0.02
now we replace it by c(100, 0.1, 0.1). Since my model is a GARCH(1,1) without any ARMA-part, I only need to set 3 parameters as descriped in the documentation ?garchSpec. After updating spec we estimate the same model:
set.seed(911)
spec#presample <- matrix(c(0.1, 0.1, 0.1), ncol = 3)
garchFit(~ garch(1, 1), data = garchSim)
with the same output:
Error Analysis:
Estimate Std. Error t value Pr(>|t|)
mu -0.02196 0.05800 -0.379 0.7049
omega 0.03567 0.02681 1.331 0.1833
alpha1 0.12074 0.04952 2.438 0.0148 *
beta1 0.84527 0.05597 15.103 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Log Likelihood:
-265.8417 normalized: -1.329209
The likelihood and estimates are identical, but notice when we simulate with the new spec:
set.seed(911)
garchSim <- garchSim(spec, n = 200, n.start = 1)
plot(garchSim)
, the extreme initial sample supplied messed up our nice simulation. But by increasing the burn.in we get:
set.seed(911)
garchSim <- garchSim(spec, n = 200, n.start = 100)
plot(garchSim)