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Hybrid stochastic local unit roots

Hybrid stochastic local unit roots
Hybrid stochastic local unit roots
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 --- oo. 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.
0304-4076
1-44
Lieberman, Offer
dc3ceb23-c100-41be-8d88-7c80625fd3fb
Phillips, Peter Charles Bonest
f67573a4-fc30-484c-ad74-4bbc797d7243
Lieberman, Offer
dc3ceb23-c100-41be-8d88-7c80625fd3fb
Phillips, Peter Charles Bonest
f67573a4-fc30-484c-ad74-4bbc797d7243

Lieberman, Offer and Phillips, Peter Charles Bonest (2019) Hybrid stochastic local unit roots. Journal of Econometrics, 1-44. (doi:10.1016/j.jeconom.2019.05.023).

Record type: Article

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 --- oo. 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.

Text
OLPCB_LSTUR_rev2_8_pcb - Accepted Manuscript
Restricted to Repository staff only until 10 October 2021.
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More information

Accepted/In Press date: 29 May 2019
e-pub ahead of print date: 10 October 2019

Identifiers

Local EPrints ID: 431557
URI: https://eprints.soton.ac.uk/id/eprint/431557
ISSN: 0304-4076
PURE UUID: e2d55cb4-419f-4e05-90a9-cc8f9d01e772
ORCID for Peter Charles Bonest Phillips: ORCID iD orcid.org/0000-0003-2341-0451

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Date deposited: 07 Jun 2019 16:30
Last modified: 19 Nov 2019 01:41

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Contributors

Author: Offer Lieberman

University divisions

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