Abstract: This article proposes omnibus goodness-of-fit tests of a parametric regression time series model. We use a general class of residual marked empirical processes as the buildingblocks for our testing problem. First, we establish a new weak convergence theorem under mild assumptions, one that extends previous existing asymptotic results and which may be of independent interest. This result allows us to study the asymptotic null distribution of the tests statistics and their asymptotic behavior against Pitman's local alternatives in a unified way. To approximate the asymptotic null distribution of test statistics we give a theoretical justification of a bootstrap procedure. Our bootstrap tests are robust to conditional higher moments of unknown form, in particular to conditional heteroskedasticity. Finally, a Monte Carlo study shows that the bootstrap and the asymptotic results provide good approximations for small sample sizes and an empirical application to the Canadian lynx data set is considered.
Key words and phrases: Canadian lynx data set, conditional mean, diagnostic tests, marked empirical processes, time series, weak convergence, wild bootstrap.