  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).
