Publication Type

Journal Article

Version

publishedVersion

Publication Date

11-2024

Abstract

New limit theory is provided for a wide class of sample variance and covariance functionals involving both nonstationary and stationary time series. Sample functionals of this type commonly appear in regression applications and the asymptotics are particularly relevant to estimation and inference in nonlinear nonstationary regressions that involve unit root, local unit root, or fractional processes. The limit theory is unusually general in that it covers both parametric and nonparametric regressions. Self-normalized versions of these statistics are considered that are useful in inference. Numerical evidence reveals interesting strong bimodality in the finite sample distributions of conventional self-normalized statistics similar to the bimodality that can arise in t-ratio statistics based on heavy tailed data. Bimodal behavior in these statistics is due to the presence of long memory innovations and is shown to persist for very large sample sizes even though the limit theory is Gaussian when the long memory innovations are stationary. Bimodality is shown to occur even in the limit theory when the long memory innovations are nonstationary. To address these complications, new self-normalized versions of the test statistics are introduced that deliver improved approximations that can be used for inference.

Discipline

Econometrics

Research Areas

Econometrics

Publication

Econometric Theory

First Page

1

Last Page

58

ISSN

0266-4666

Identifier

10.1017/S0266466624000276

Publisher

Cambridge University Press

Copyright Owner and License

Authors-CC-BY

Additional URL

https://doi.org/10.1017/S0266466624000276

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