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I managed to forecast a GARCH model yesterday and run a Monte Carlo simulation on R. Nevertheless, I can't do the same with an ARMA-GARCH. I tested 4 different method but without achieving an ARMA-GARCH simulation with my data.

The packages and the data I used:

library(quantmod)
library(tseries)
library(TSA)
library(betategarch)
library(mcsm)
library(PerformanceAnalytics)
library(forecast)
library(fGarch)
library(GEVStableGarch)

getSymbols("DEXB.BR",from="2005-07-01", to="2015-07-01")
STOCK = DEXB.BR
STOCK.rtn=diff(STOCK[,6] )
STOCK.diff = STOCK.rtn[2:length(STOCK.rtn)]
ARI_2_1=arima(STOCK[,6],order=c(2,1,1))
GA_1_1=garch(ARI_2_1$residuals, order = c(1,1))

First tested method

specifi = garchSpec(model = list(ar = c(0.49840, -0.0628), ma =c(-0.4551), omega = 8.393e-08, alpha = 1.356e-01, beta = 8.844e-01))

garchSim(spec = specifi, n = 500, n.start = 200, extended = FALSE)

This lead to a "NaN" forecast.

garchSim(spec = specifi, n = 500)

n=1000 armagarch.sim_1 = rep(0,n) armagarch.sim_50 = rep(0,n) armagarch.sim_100 = rep(0,n) for(i in 1:n) { armagarch.sim=garchSim(spec = specifi, n = 500, n.start = 200, extended = FALSE) armagarch.sim_1[i] = armagarch.sim[1] armagarch.sim_50[i] = armagarch.sim[50] armagarch.sim_100[i] = armagarch.sim[100]

}

Second tested method

GSgarch.Sim(N = 500, mu = 0, a = c(0.49840, -0.0628), b = c(-0.4551), omega = 8.393e-08, alpha = c(1.356e-01), gm = c(0), beta = c(8.844e-01), cond.dist = "norm")

This part works.

n=10000

Garmagarch.sim_1 = rep(0,n)
Garmagarch.sim_50 = rep(0,n)
Garmagarch.sim_100 = rep(0,n)

for(i in 1:n)
{
    Garmagarch.sim= GSgarch.Sim(N = 500, mu = 0, a = c(0.49840, -0.0628), b = c(-0.4551),omega = 8.393e-08, alpha = c(1.356e-01), gm = c(0), beta c(8.844e-01), cond.dist = "norm")

    Garmagarch.sim_1[i] = Garmagarch.sim[1]
    Garmagarch.sim_50[i] = Garmagarch.sim[50]
    Garmagarch.sim_100[i] = Garmagarch.sim[100]

}

The simulation runs but

> Garmagarch.sim[1]
$model
[1] "arma(2,1)-aparch(1,1) ## Intercept:FALSE"

and

> Garmagarch.sim[50]
$<NA>
NULL

Third tested method

ga_arma = garch.sim(alpha=c(8.393e-08,1.356e-01),beta =8.844e-01 ,n=500, ntrans=200)

This lead to

Error in garch.sim(alpha = c(8.393e-08, 0.1356), beta = 0.8844, n = 500,  : 
  Check model: it does not have finite variance


arima.sim(ARI_2_1, 500, innov = ga_arma ,n.start = 200)

And this to

Error in arima.sim(ARI_2_1, 500, innov = ga_arma, n.start = 200) : 
  la partie 'ar' du mopdèle n'est pas stationaire

which mean that the 'ar' part of the model isn't stationnary.

Fourth tested method

forecast(ARI_2_1, h = 500, bootstrap = TRUE, npaths=200)

This one actually works but I don't know how to add the GARCH component.

forecast(specifi, h = 500, bootstrap = TRUE, npaths=200)

Thanks !

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