  In this paper we consider the problem of constructing confidence intervals
for coefficients of martingale regression models (in particular, time series
models) after variable selection. Although constructing confidence intervals
are common practice in statistical analysis, it is challenging in our framework
due to the data-dependence of the selected model and the correlation among the
variables being selected and not selected. We first introduce estimators for
the selected coefficients and show that it is consistent under martingale
regression model, in which the observations can be dependent and the errors can
be heteroskedastic. Then we use the estimators together with a resampling
approach to construct confidence intervals. Our simulation results show that
our approach outperforms other existing approaches in various data structures.
