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Robust Inference on Infinite and Growing Dimensional Regression

Abhimanyu Gupta and Myung Hwan Seo

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Abstract: We develop a class of tests for a growing number of restrictions in infinite and increasing order time series models such as infinite-order autoregression, nonparametric sieve regression and multiple regression with growing dimension. Examples include the Chow test, Andrews and Ploberger (1994) type exponential tests, and testing of general linear restrictions of growing rank $p$. Notably, our tests introduce a new scale correction to the conventional quadratic forms that are recentered and normalized to account for diverging $p$. This correction accounts for a high-order long-run variance that emerges as $p$ grows with sample size in time series regression. Furthermore, we propose a bias correction via a null-imposed bootstrap to control finite sample bias without sacrificing power unduly. A simulation study stresses the importance of robustifying testing procedures against the high-order long-run variance even when $p$ is moderate. The tests are illustrated with an application to the oil regression in Hamilton (2003).

Date: 2019-11, Revised 2021-03
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Handle: RePEc:arx:papers:1911.08637