help archqq-------------------------------------------------------------------------------

Q-Q plots and tests to assess distributional assumptions for ARCH models

Syntax

archqq[varname] [if] [in] [,distribution(dist[#])nographnotestjb]

Description

archqqis primarily for use afterarchbut can also be applied to an arbitrary variable. It displays Q-Q plots of the standardized residuals from an ARCH model against a standard normal, t-distribution normalized to variance 1 or the GED distribution. The distribution (and degrees of freedom for a t-distribution or shape parameter for the GED) is the one used witharchif not specified explicitly.Additionally, the data and assumed moments, mean, variance, skewness and kurtosis and.the Kolmogorov-Smirnov test for distribution are reported. In addition the Jarque-Bera test for normality is reported if the assumed distribution is normal. Optionally, a Jarque-Bera type test generalized to allow other null hypothesis than a normal distribution can be reported. Note that the properties of the generalized test are unknown. In particular, the test appears to have very low power when the alternative is a distribution with thinner tails than the null.

If a variable is specified the comparison distribution is scaled to the data mean and variance.

Options

optionDescription -------------------------------------------------------------------------

distribution(dist[#])Use thedistdistribution with parameter#.distcan be onegaussian,normal,torged.gaussianandnormalare synonyms. The second argument specifies the degrees of freedom fortor the shape parameter forgedand is not allowed withgaussianandnormal. The default isgaussianif a variable is specified, otherwise the default is taken from thearchestimation results.

nographSuppress display of Q-Q plot.

nottestSuppress display of moments and test statistics.

jbForce calculation of Jarque-Bera type test with non-normal distributions.-------------------------------------------------------------------------

ExamplesSetup

. webuse wpi1Fit GARCH(1,1) under normality and display Q-Q plot

. arch D.ln_wpi, arch(1) garch(1). archqqFit GARCH(1,1) with a t-distribution and display Q-Q plot

. arch D.ln_wpi, arch(1) garch(1) dist(t). archqq

AuthorSune Karlsson, Örebro University, Sweden sune.karlsson@oru.se