[R] GMM with covariance moment condicion

[peterko]

hello

I have covariance stacionary proces, and i want to estimate some parameter
of this proces via gmm.

My problem is with write "g" -function.
0 order autocovariance is not problem
1 and higher order autocavariance are problem, because add order from 0 mean
that I "loose" one "observacion"


if I have 100 observation and i am going to use mean, variance and first
autocovariance
and fit one parameter !
g<- function(theta,x) 
  {

      m1<-(P1-x)  
      m2<-(P2-(x-P1)^2)
      m3<-(P3-(???))
      f <- cbind(m1,m2,m3)
      return(f) }


where P1,P2,P3 are formulas for mean, variance and first autocovariance via
my parameter

my question is how to define ???
i think about something like this :
y<-x[2:length(x)]
x<-x[-(length(x))]
       m1<-(P1-x)  
      m2<-(P2-(x-P1)^2)
      m3<-(P3-(x-P1)*(y-P1))
but here i have to lost 1 observacion, what is problem when i call gmm:

rad<-arima.sim(n=200,list(ar=0.5), sd=1)
tet<-gmm(g,rad,t0=c(0))

any idea ? thanks
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