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).

Date: 2019-11, Revised 2023-04
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Journal Article: Robust Inference on Infinite and Growing Dimensional Time‐Series Regression (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1911.08637

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