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), which 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).