Publication Type

Journal Article

Version

publishedVersion

Publication Date

7-2021

Abstract

We introduce a generalization of the popular local‐to‐unity model of time series persistence by allowing for p autoregressive (AR) roots and p − 1 moving average (MA) roots close to unity. This generalized local‐to‐unity model, GLTU(p), induces convergence of the suitably scaled time series to a continuous time Gaussian ARMA(p,p − 1) process on the unit interval. Our main theoretical result establishes the richness of this model class, in the sense that it can well approximate a large class of processes with stationary Gaussian limits that are not entirely distinct from the unit root benchmark. We show that Campbell and Yogo's (2006) popular inference method for predictive regressions fails to control size in the GLTU(2) model with empirically plausible parameter values, and we propose a limited‐information Bayesian framework for inference in the GLTU(p) model and apply it to quantify the uncertainty about the half‐life of deviations from purchasing power parity.

Keywords

Continuous time ARMA process, convergence, approximability

Discipline

Econometrics

Research Areas

Econometrics

Publication

Econometrica

Volume

89

Issue

4

First Page

1825

Last Page

1854

ISSN

0012-9682

Identifier

10.3982/ECTA17944

Publisher

Econometric Society: Econometrica

Copyright Owner and License

Publisher

Additional URL

https://doi.org/10.3982/ECTA17944

Download

Included in

Econometrics Commons

Share

COinS