Robust Inference on Infinite and Growing Dimensional Time Series Regression
Abstract
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).
- Publication:
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arXiv e-prints
- Pub Date:
- November 2019
- DOI:
- 10.48550/arXiv.1911.08637
- arXiv:
- arXiv:1911.08637
- Bibcode:
- 2019arXiv191108637G
- Keywords:
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- Economics - Econometrics
- E-Print:
- 58 pages, 7 figures