Boundary limit theory for functional local to unity regression

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 tha...

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Main Authors: BYKHOVSKAYA, Anna, PHILLIPS, Peter C. B.
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Language:English
Published: Institutional Knowledge at Singapore Management University 2018
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Online Access:https://ink.library.smu.edu.sg/soe_research/2343
https://ink.library.smu.edu.sg/context/soe_research/article/3342/viewcontent/Boundary_Limit_Theory_Functional_sv.pdf
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spelling sg-smu-ink.soe_research-33422020-01-30T04:01:30Z Boundary limit theory for functional local to unity regression BYKHOVSKAYA, Anna PHILLIPS, Peter C. B. 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. 2018-07-01T07:00:00Z text application/pdf https://ink.library.smu.edu.sg/soe_research/2343 info:doi/10.1111/jtsa.12285 https://ink.library.smu.edu.sg/context/soe_research/article/3342/viewcontent/Boundary_Limit_Theory_Functional_sv.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Economics eng Institutional Knowledge at Singapore Management University Boundary asymptotics functional local unit root local to unity sequential limits simultaneous limits unit root model Econometrics
institution Singapore Management University
building SMU Libraries
continent Asia
country Singapore
Singapore
content_provider SMU Libraries
collection InK@SMU
language English
topic Boundary asymptotics
functional local unit root
local to unity
sequential limits
simultaneous limits
unit root model
Econometrics
spellingShingle Boundary asymptotics
functional local unit root
local to unity
sequential limits
simultaneous limits
unit root model
Econometrics
BYKHOVSKAYA, Anna
PHILLIPS, Peter C. B.
Boundary limit theory for functional local to unity regression
description 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.
format text
author BYKHOVSKAYA, Anna
PHILLIPS, Peter C. B.
author_facet BYKHOVSKAYA, Anna
PHILLIPS, Peter C. B.
author_sort BYKHOVSKAYA, Anna
title Boundary limit theory for functional local to unity regression
title_short Boundary limit theory for functional local to unity regression
title_full Boundary limit theory for functional local to unity regression
title_fullStr Boundary limit theory for functional local to unity regression
title_full_unstemmed Boundary limit theory for functional local to unity regression
title_sort boundary limit theory for functional local to unity regression
publisher Institutional Knowledge at Singapore Management University
publishDate 2018
url https://ink.library.smu.edu.sg/soe_research/2343
https://ink.library.smu.edu.sg/context/soe_research/article/3342/viewcontent/Boundary_Limit_Theory_Functional_sv.pdf
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