High-dimensional time series arise in several contemporary applications in finance and engineering. In ARMA type models, assuming sparsity, it is common to use regularization based methods such as LASSO and SCAD to perform model/variable selection. However, the effect of performing model selection on the resulting inference is largely unknown. In this presentation, we focus on stationary ARMA-type models and describe a new regeneration based inferential procedure that accounts for model selection uncertainty. We establish the consistency and asymptotic normality of the proposed post-selection estimators. Simulation results and data analyses are included to demonstrate the proposed methods. We bring to fore the importance of the return times over regeneration times of the Markov chain associated with these processes in the current setting.