Hi,
I'm trying to interpret the following results, with respect to "normality test
using the over identifying moment conditions"
where returns have normal distribution
with parameter mu,sd
and i have 4 moment conditions
>E[r-mu/sd]=0
>E[(r-mu)^2/sd-1]=0
>E[(r-mu)^3/sd^3]=0
>E[(r-mu)^4/sd^4-3]=0
output..
gel(g = g, x = returns, tet0 = c(f3$estimate[1], f3$estimate[2]))
Type of GEL: EL
Coefficients:
Estimate Std. Error t value Pr(>|t|)
mean -0.01168 0.05614 -0.20805 0.83519
sd 1.77591 0.03965 44.79218 0.00000
Lambdas:
Estimate Std. Error t value Pr(>|t|)
Lambda[1] -0.09743 0.03912 -2.49028 0.01276
Lambda[2] 0.65728 0.02443 26.90505 0.00000
Lambda[3] 0.03247 0.01304 2.48961 0.01279
Lambda[4] -0.10954 0.00407 -26.90423 0.00000
Over-identifying restrictions tests: degrees of freedom is 2
statistics p-value
LR test 2.3341e+02 2.0730e-51
LM test 7.2417e+02 5.5954e-158
J test 7.2417e+02 5.5954e-158
Convergence code for the coefficients: 0
Convergence code for the lambdas: 0
does the J-test p-value rejecting the null E[g(theta,x)]=0, and which moment
condition is true under normality
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