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

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


Syntax

        archqq [varname] [if] [in] [, distribution(dist [#]) nograph notest
                         jb]

Description

archqq is primarily for use after arch but 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 with arch if 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

    option                  Description
    -------------------------------------------------------------------------

    distribution(dist [#])  Use the dist distribution with parameter #.  dist
                              can be one gaussian, normal, t or ged. gaussian
                              and normal are synonyms. The second argument
                              specifies the degrees of freedom for t or the
                              shape parameter for ged and is not allowed with
                              gaussian and normal. The default is gaussian if
                              a variable is specified, otherwise the default
                              is taken from the arch estimation results.

    nograph                 Suppress display of Q-Q plot.

    nottest                 Suppress display of moments and test statistics.

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

    -------------------------------------------------------------------------

Examples

    Setup
        . webuse wpi1

    Fit GARCH(1,1) under normality and display Q-Q plot
        . arch D.ln_wpi, arch(1) garch(1)
        . archqq

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

Author

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