This paper develops specification diagnostics for discrete time durati
on models which are based on the martingale theory of stochastic proce
sses. The methods can be applied to parametric grouped data duration m
odels with time-varying covariates, right censoring, and which account
for unobserved heterogeneity. A residual process is defined such that
, under the correct model specification, the process is (approximately
) a martingale difference sequence. Chi-square tests based on these re
siduals are derived. Results from Monte Carlo simulations are presente
d.