Publication Type
Journal Article
Version
submittedVersion
Publication Date
7-2018
Abstract
This article studies functional local unit root models (FLURs) in which the autoregressive coefficient may vary with time in the vicinity of unity. We extend conventional local to unity (LUR) models by allowing the localizing coefficient to be a function which characterizes departures from unity that may occur within the sample in both stationary and explosive directions. Such models enhance the flexibility of the LUR framework by including break point, trending, and multidirectional departures from unit autoregressive coefficients. We study the behavior of this model as the localizing function diverges, thereby determining the impact on the time series and on inference from the time series as the limits of the domain of definition of the autoregressive coefficient are approached. This boundary limit theory enables us to characterize the asymptotic form of power functions for associated unit root tests against functional alternatives. Both sequential and simultaneous limits (as the sample size and localizing coefficient diverge) are developed. We find that asymptotics for the process, the autoregressive estimate, and its t-statistic have boundary limit behavior that differs from standard limit theory in both explosive and stationary cases. Some novel features of the boundary limit theory are the presence of a segmented limit process for the time series in the stationary direction and a degenerate process in the explosive direction. These features have material implications for autoregressive estimation and inference which are examined in the article.
Keywords
Boundary asymptotics, functional local unit root, local to unity, sequential limits, simultaneous limits, unit root model
Discipline
Econometrics
Research Areas
Econometrics
Publication
Journal of Time Series Analysis
Volume
39
Issue
4
First Page
523
Last Page
562
ISSN
0143-9782
Identifier
10.1111/jtsa.12285
Publisher
Wiley
Embargo Period
1-29-2020
Citation
BYKHOVSKAYA, Anna and PHILLIPS, Peter C. B..
Boundary limit theory for functional local to unity regression. (2018). Journal of Time Series Analysis. 39, (4), 523-562.
Available at: https://ink.library.smu.edu.sg/soe_research/2343
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1111/jtsa.12285