## S3 method for class 'gel'
fitted(object, ...)
## S3 method for class 'gmm'
fitted(object, ...)

# GEL can deal with endogeneity problems

n = 200
phi<-c(.2,.7)
thet <- 0.2
sd <- .2
set.seed(123)
x <- matrix(arima.sim(n = n, list(order = c(2,0,1), ar = phi, ma = thet, sd = sd)), ncol = 1)

y <- x[7:n]
ym1 <- x[6:(n-1)]
ym2 <- x[5:(n-2)]
H <- cbind(x[4:(n-3)], x[3:(n-4)], x[2:(n-5)], x[1:(n-6)])
g <- y ~ ym1 + ym2
x <- H

res <- gel(g, x, c(0,.3,.6))
plot(y, main = "Fitted ARMA with GEL")
lines(fitted(res), col = 2)

# GMM is like GLS for linear models without endogeneity problems

set.seed(345)
n = 200
phi<-c(.2,.7)
thet <- 0
sd <- .2
x <- matrix(arima.sim(n = n, list(order = c(2,0,1), ar = phi, ma = thet, sd = sd)), ncol = 1)
y <- 10 + 5*rnorm(n) + x

res <- gmm(y ~ x, x)
plot(x, y, main = "Fitted model with GMM")
lines(x, fitted(res), col = 2)
legend("topright", c("Y","Yhat"), col = 1:2, lty = c(1,1))