On the use of shrinkage estimators in macroeconometric modeling and forecasting

In the last years a growing °ow of information in the ¯eld of macroeconomy has been collected in very large databases. It is well known nevertheless that, when a large number of series is available standard statistical tools do not work well. This thesis proposes new estimators for high dimensional systems, that are an optimally weighted average of two already existing estimators, a traditional unbiased one, su®ering of a large estimation error, and a target one, having a lot of bias coming from a misspeci¯ed structural assumption, but little in terms of variance. This method is generally known as shrinkage. We derive two di®erent estimators connected with large dimensional systems. First a new estimator for the coe±cient matrix in a large dimensional vector autoregressive process (VAR) is proposed. It shows a better performance in forecasting macroeconomic time series than a set of existing estimators, including factor models and bayesian shrinkage estimators. A new estimator is also built for the variance covariance matrix in high dimensional systems. This new estimator is used to test for the presence of Serial Correlation Common Features (SCCF) in a multivariate setting involving many, noisy, and collinear time series. It shows a good performance in terms of empirical size if compared to the already existing tool of Canonical Correlation Analysis (CCA).