Hybrid Stochastic Local Unit Roots

Offer Lieberman and Peter Phillips
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Offer Lieberman: Bar-Ilan University

No 2113, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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 tends to 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 are explored in an application to the spreads on US investment grade corporate debt.

Keywords: Autoregression; Nonlinear diffusion; Stochastic unit roo; Time-varying coefficient (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Pages: 28 pages
Date: 2017-11
New Economics Papers: this item is included in nep-ets
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Citations: View citations in EconPapers (2)

Published in Journal of Econometrics, (February 2020), 215(1): 257-285

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