Implements the GMM Orthogonality Test of Hansen.
GMMTest(z, lags = 1, skew=0, kurt=3, conf.level = 0.95)A list with the following items:
The matrix of the joint tests.
The matrix of the individual moment tests.
The Null Hypothesis.
Whether to reject or not the Null given the conf.level.
A numeric vector the standardized residuals.
The number of lags to test for.
The skewness of the standardized residuals (derived from the estimated model). This can be either a scalar or numeric vector the same size as z.
The kurtosis (not excess) of the standardized residuals (derived from the estimated model). This can be either a scalar or numeric vector the same size as z.
The confidence level at which the Null Hypothesis is evaluated.
Alexios Ghalanos
This is a mispecification test based on Hansen's GMM procedure. Under a correctly specified model, certain population moment conditions should be satisfied and hold in the sample using the standardized residuals. The moment conditions can be tested both individually using a t-test or jointly using a Wald test (the vignette gives more details). The test returns a matrix (moment.mat) containing the first 4 moments statistics, their standard errors and t-values (2-sided t-test with alternative hypothesis that the value is not equal to zero). The matrix of joint conditions (joint.mat) contains the t-values and critical values of ‘Q2’, ‘Q3’ and ‘Q4’ representing the autocorrelation, given the chosen lags in the second, third and fourth moments and distributed as chi-squared with n.lag d.o.f, and the joint test (‘J’) for all moment conditions distributed chi-squared with 4+(n.lagx3) d.o.f.
Hansen, L. (1982), Large Sample Properties of Generalized Method of Moments Estimators, Econometrica, 50(4), 1029--1054.