Robust Inference on Infinite and Growing Dimensional Time Series Regression

We develop a class of tests for time series models such as multiple regression with growing dimension, infinite-order autoregression and nonparametric sieve regression. Examples include the Chow test and general linear restriction tests of growing rank $p$. Employing such increasing $p$ asymptotics, we introduce a new scale correction to conventional test statistics which accounts for a high-order long-run variance (HLV) that emerges as $p$ grows with sample size. We also propose a bias correction via a null-imposed bootstrap to alleviate finite sample bias without sacrificing power unduly. A simulation study shows the importance of robustifying testing procedures against the HLV even when $p$ is moderate. The tests are illustrated with an application to the oil regressions in Hamilton (2003).