Journal of Economic Literature (JEL) Code(s)
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 are explored in an application to the spreads on US investment grade corporate debt.
Lieberman, Offer and Phillips, Peter C.B., "Hybrid Stochastic Local Unit Roots" (2017). Cowles Foundation Discussion Papers. 165.