Robust Inference on Infinite and Growing Dimensional Time Series Regression

TL;DR

This paper introduces robust testing methods for high-dimensional and infinite-dimensional time series models, incorporating scale correction and bootstrap bias adjustment to improve inference accuracy.

Contribution

It develops new tests for growing-dimensional time series models that account for high-order long-run variance and finite sample bias, enhancing robustness and applicability.

Findings

Scale correction improves test accuracy with increasing p

Bootstrap bias correction reduces finite sample bias

Tests perform well in simulations and real oil regression data

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).