In the process of autoregressive modeling (AR(p,q)), we do not know the true order of the model generating the data. In fact it will usually be the case that there is no true AR(p,q) model, in which case our goal is simply to find one that represents the data optimally in some sense. To handle this problem, a variety of information criteria have already been proposed, each with a different background. In this thesis, we consider the problem of time series model selection and investigate the performance of a number of proposed information criteria. First, we give the most common selection criteria to select the best model and we study its properties. Then, we will present and investigate some corrected versions of the Kullback information criterion KIC, based on Kullback's symmetric divergence, for model selection in univariate and vector autoregressive models. Moreover, a large simulation study will be undertaken to compare the performance of the studied criteria.