Publication Type

Journal Article

Version

submittedVersion

Publication Date

3-2020

Abstract

Two approaches have dominated formulations designed to capture small departures from unit root autoregressions. The first involves deterministic departures that include local-to-unity (LUR) and mildly (or moderately) integrated (MI) specifications where departures shrink to zero as the sample size n -> infinity. The second approach allows for stochastic departures from unity, leading to stochastic unit root (STUR) specifications. This paper introduces a hybrid local stochastic unit root (LSTUR) specification that has both LUR and STUR components and allows for endogeneity in the time varying coefficient that introduces structural elements to the autoregression. This hybrid model generates trajectories that, upon normalization, have non-linear diffusion limit processes that link closely to models that have been studied in mathematical finance, particularly with respect to option pricing. It is shown that some LSTUR parameterizations have a mean and variance which are the same as a random walk process but with a kurtosis exceeding 3, a feature which is consistent with much financial data. We develop limit theory and asymptotic expansions for the process and document how inference in LUR and STUR autoregressions is affected asymptotically by ignoring one or the other component in the more general hybrid generating mechanism. In particular, we show how confidence belts constructed from the LUR model are affected by the presence of a STUR component in the generating mechanism. The import of these findings for empirical research is explored in an application to the spreads on US investment grade corporate debt.

Keywords

Autoregression, Local unit root, Nonlinear diffusion, Stochastic unit root, Time-varying coefficient

Discipline

Econometrics

Research Areas

Econometrics

Publication

Journal of Econometrics

Volume

215

Issue

1

First Page

257

Last Page

285

ISSN

0304-4076

Identifier

10.1016/j.jeconom.2019.05.023

Publisher

Elsevier: 24 months

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.1016/j.jeconom.2019.05.023

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