Hybrid stochastic local unit roots

Offer Lieberman, Peter C.B. Phillips

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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→∞. 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.

Original languageEnglish
Pages (from-to)257-285
Number of pages29
JournalJournal of Econometrics
Issue number1
StatePublished - Mar 2020

Bibliographical note

Publisher Copyright:
© 2019 Elsevier B.V.


Support from Israel Science Foundation grant No. 1182-17 and from the Sapir Center in Tel Aviv University are gratefully acknowledged.Research support from the Kelly Foundation, University of Auckland, New Zealand is gratefully acknowledged.

FundersFunder number
Kelly Foundation
Sapir Center in Tel Aviv University
University of Auckland
Israel Science Foundation1182-17


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


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