  This paper proposes new parametric model adequacy tests for possibly
nonlinear and nonstationary time series models with noncontinuous data
distribution, which is often the case in applied work. In particular, we
consider the correct specification of parametric conditional distributions in
dynamic discrete choice models, not only of some particular conditional
characteristics such as moments or symmetry. Knowing the true distribution is
important in many circumstances, in particular to apply efficient maximum
likelihood methods, obtain consistent estimates of partial effects and
appropriate predictions of the probability of future events. We propose a
transformation of data which under the true conditional distribution leads to
continuous uniform iid series. The uniformity and serial independence of the
new series is then examined simultaneously. The transformation can be
considered as an extension of the integral transform tool for noncontinuous
data. We derive asymptotic properties of such tests taking into account the
parameter estimation effect. Since transformed series are iid we do not require
any mixing conditions and asymptotic results illustrate the double simultaneous
checking nature of our test. The test statistics converges under the null with
a parametric rate to the asymptotic distribution, which is case dependent,
hence we justify a parametric bootstrap approximation. The test has power
against local alternatives and is consistent. The performance of the new tests
is compared with classical specification checks for discrete choice models.
