gmm_test function

GMM Orthogonality Test

The GMM orthogonality test of Hansen (1982).

gmm_test(x, lags = 1, skewness = 0, kurtosis = 3, ...)

Arguments

• x: a series representing the standardized residuals of some estimated model.
• lags: the lags for the co-moment test.
• skewness: the skewness of the estimated model residuals.
• kurtosis: the kurtosis of the estimated model residuals.
• ...: not currently used.

Returns

An object of class tstest.gmm which has a print and as_flextable method.

Details

For parametric models estimated with a particular distribution, the skewness and kurtosis should flow from the distributional model. See for example dskewness and dkurtosis.

Examples

library(tsgarch)
library(tsdistributions)
library(data.table)
library(xts)
data("spy")
spyr <- na.omit(diff(log(spy)))
spec <- garch_modelspec(spyr, model = "egarch", order = c(2,1), constant = TRUE,
distribution = "jsu")
mod <- estimate(spec)
skewness <- dskewness("jsu", skew = coef(mod)["skew"], shape = coef(mod)["shape"])
# kurtosis is dkurtosis is the excess over the Normal (3) so we add back 3
# since the test takes the actual not excess kurtosis.
kurtosis <- dkurtosis("jsu", skew = coef(mod)["skew"], shape = coef(mod)["shape"]) + 3
test <- gmm_test(residuals(mod, standardize = TRUE), lags = 2, skewness = skewness,
kurtosis = kurtosis)
print(test, collapse = TRUE, include.decision = TRUE)

References

\insertRef Hansen1982tstests