# GMMTest: The GMM Orthogonality Test of Hansen In rugarch: Univariate GARCH Models

## Description

Implements the GMM Orthogonality Test of Hansen.

## Usage

 `1` ```GMMTest(z, lags = 1, skew=0, kurt=3, conf.level = 0.95) ```

## Arguments

 `z` A numeric vector the standardized residuals. `lags` The number of lags to test for. `skew` 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. `kurt` 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. `conf.level` The confidence level at which the Null Hypothesis is evaluated.

## Details

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.

## Value

A list with the following items:

 `joint.mat` The matrix of the joint tests. `moment.mat` The matrix of the individual moment tests. `H0` The Null Hypothesis. `Decision` Whether to reject or not the Null given the conf.level.

Alexios Ghalanos

## References

Hansen, L. (1982), Large Sample Properties of Generalized Method of Moments Estimators, Econometrica, 50(4), 1029–1054.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```## Not run: data(dji30ret) spec = ugarchspec(mean.model = list(armaOrder = c(1,1), include.mean = TRUE), variance.model = list(model = "gjrGARCH"), distribution.model = "sstd") fit = ugarchfit(spec, data = dji30ret[, 1, drop = FALSE]) z = residuals(fit)\/sigma(fit) skew = dskewness("sstd",skew = coef(fit)["skew"], shape= coef(fit)["shape"]) # add back 3 since dkurtosis returns the excess kurtosis kurt = 3+dkurtosis("sstd",skew = coef(fit)["skew"], shape= coef(fit)["shape"]) print(GMMTest(z, lags = 1, skew=skew, kurt=kurt)) ## End(Not run) ```

rugarch documentation built on May 29, 2017, 10:39 a.m.