Econometric inference in models with nonstationary time series

We investigate the finite-sample behaviour of the OLS estimator in vector autoregressive (VAR) models. The data generating process is a purely nonstationary first-order VAR. We derive response surfaces for OLS bias and variance in terms of VAR dimensions under over-parameterized models: we include deterministic components and excess autoregressive lags. Correction factors are introduced that minimise the mean squared error (MSE) of the OLS estimator. Our analysis extends one of the main finite-sample multivariate analytical bias results of Abadir, Hadri and Tzavalis (1999), generalises the univariate variance and MSE results of Abadir (1995) to a multivariate setting, and complements various asymptotic studies.
The distribution of unit root test statistics generally contains nuisance parameters that correspond to the error correlation structure. The presence of such nuisance parameters can lead to serious size distortion. To address this issue, we adopt an approach based on the characterization of the class of asymptotically similar critical regions for the unit root hypothesis and the application of two new optimality criteria for the choice of a test within this class. The correlation structure of the innovation sequence takes the form of a moving average process, the order of which is determined by information criteria. Limit distribution theory for the resulting test statistics is developed and simulation evidence suggests that our statistics have substantially reduced size while retaining good power properties.
Stock return predictability is a fundamental issue in asset pricing. The conclusions of empirical analyses on the existence of stock return predictability vary according to the time series properties of the predictors. The degree of persistence uncertainty of these variables, motivates the use of the most general possible modelling framework. This possibility is provided by the IVX methodology developed by Phillips and Magdalinos (2009). This method is modified to allow for an intercept in the predictive regressions. The modified IVX approach yields chi-squared inference for general linear restrictions on the regression coefficients that is robust to the regressors’ degree of persistence. The advantages offered by the application of the modified IVX methodology are highlighted by our empirical study.