Model selection has an important impact on subsequent inference+ Ignoring the model selection step leads to invalid inference+ We discuss some intricate aspects of data-driven model selection that do not seem to have been widely appreciated in the literature+ We debunk some myths about model selection, in particular the myth that consistent model selection has no effect on subsequent inference asymp-totically+ We also discuss an "impossibility" result regarding the estimation of the finite-sample distribution of post-model-selection estimators+

Testing restrictions on regression coefficients in linear models often requires correcting the conventional F-test for potential heteroskedasticity or autocorrelation amongst the disturbances, leading to so-called heteroskedasticity and autocorrelation robust test procedures. These procedures have been developed with the purpose of attenuating size distortions and power deficiencies present for the uncorrected F-test. We develop a general theory to establish positive as well as negative finite-sample results concerning the size and power properties of a large class of heteroskedasticity and autocorrelation robust tests. Using these results we show that nonparametrically as well as parametrically corrected F-type tests in time series regression models with stationary disturbances have either size equal to one or nuisance-infimal power equal to zero under very weak assumptions on the covariance model and under generic conditions on the design matrix. In addition we suggest an adjustment procedure based on artificial regressors. This adjustment resolves the problem in many cases in that the so-adjusted tests do not suffer from size distortions. At the same time their power function is bounded away from zero. As a second application we discuss the case of heteroskedastic disturbances.

The asymptotic properties of parameter estimators which are based on a model that has been selected by a model selection procedure are investigated. In particular, the asymptotic distribution is derived and the effects of the model selection process on subsequent inference are illustrated.

The aim of the research is analysis of short-and long-term international relations between stock exchanges in Central and Eastern Europe. The analysis is provided in 3 stages. In the first step the order of the variables integration is examined. In the second stage short-run relationships for pairs of indexes are analyzed using Granger causality test. In the last step long-run relationships for pairs of indexes are examined applying Johansen cointegration method. K e y w o r d s: Emerging Markets, Equity CEE Markets, cointegration, Granger Causality, long-run relationships, short-run relationships. J E L Classification: G15.

We consider the problem of estimating the conditional distribution of a post-model-selection estimator where the conditioning is on the selected model. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by a model selection criterion such as AIC or by a hypothesis testing procedure) and then estimating the parameters in the selected model (e.g., by least-squares or maximum likelihood), all based on the same data set. We show that it is impossible to estimate this distribution with reasonable accuracy even asymptotically. In particular, we show that no estimator for this distribution can be uniformly consistent (not even locally). This follows as a corollary to (local) minimax lower bounds on the performance of estimators for this distribution. Similar impossibility results are also obtained for the conditional distribution of linear functions (e.g., predictors) of the post-model-selection estimator.