st: normality test using the over identifying moment conditions

[Usman Gilani <u.gilani@icloud.com>]

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