Threshold regression asymptotics: From the compound Poisson process to two-sided Brownian motion

The asymptotic distribution of the least squares estimator in threshold regression is expressed in terms of a compound Poisson process when the threshold effect is fixed and as a functional of two-sided Brownian motion when the threshold effect shrinks to zero. This paper explains the relationship b...

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Main Authors: YU, Ping, 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/2353
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spelling sg-smu-ink.soe_research-33522020-02-28T06:27:00Z Threshold regression asymptotics: From the compound Poisson process to two-sided Brownian motion YU, Ping PHILLIPS, Peter C. B. The asymptotic distribution of the least squares estimator in threshold regression is expressed in terms of a compound Poisson process when the threshold effect is fixed and as a functional of two-sided Brownian motion when the threshold effect shrinks to zero. This paper explains the relationship between this dual limit theory by showing how the asymptotic forms are linked in terms of joint and sequential limits. In one case, joint asymptotics apply when both the sample size diverges and the threshold effect shrinks to zero, whereas sequential asymptotics operate in the other case in which the sample size diverges first and the threshold effect shrinks subsequently. The two operations lead to the same limit distribution, thereby linking the two different cases. The proofs make use of ideas involving limit theory for sums of a random number of summands. 2018-11-01T07:00:00Z text application/pdf https://ink.library.smu.edu.sg/soe_research/2353 info:doi/10.1016/j.econlet.2018.08.039 https://ink.library.smu.edu.sg/context/soe_research/article/3352/viewcontent/2Asys_av.pdf https://ink.library.smu.edu.sg/context/soe_research/article/3352/filename/0/type/additional/viewcontent/2Asys_mmc1.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Economics eng Institutional Knowledge at Singapore Management University Threshold regression Sequential asymptotics Doob's martingale inequality Compound Poisson process Brownian motion Econometrics
institution Singapore Management University
building SMU Libraries
continent Asia
country Singapore
Singapore
content_provider SMU Libraries
collection InK@SMU
language English
topic Threshold regression
Sequential asymptotics
Doob's martingale inequality
Compound Poisson process
Brownian motion
Econometrics
spellingShingle Threshold regression
Sequential asymptotics
Doob's martingale inequality
Compound Poisson process
Brownian motion
Econometrics
YU, Ping
PHILLIPS, Peter C. B.
Threshold regression asymptotics: From the compound Poisson process to two-sided Brownian motion
description The asymptotic distribution of the least squares estimator in threshold regression is expressed in terms of a compound Poisson process when the threshold effect is fixed and as a functional of two-sided Brownian motion when the threshold effect shrinks to zero. This paper explains the relationship between this dual limit theory by showing how the asymptotic forms are linked in terms of joint and sequential limits. In one case, joint asymptotics apply when both the sample size diverges and the threshold effect shrinks to zero, whereas sequential asymptotics operate in the other case in which the sample size diverges first and the threshold effect shrinks subsequently. The two operations lead to the same limit distribution, thereby linking the two different cases. The proofs make use of ideas involving limit theory for sums of a random number of summands.
format text
author YU, Ping
PHILLIPS, Peter C. B.
author_facet YU, Ping
PHILLIPS, Peter C. B.
author_sort YU, Ping
title Threshold regression asymptotics: From the compound Poisson process to two-sided Brownian motion
title_short Threshold regression asymptotics: From the compound Poisson process to two-sided Brownian motion
title_full Threshold regression asymptotics: From the compound Poisson process to two-sided Brownian motion
title_fullStr Threshold regression asymptotics: From the compound Poisson process to two-sided Brownian motion
title_full_unstemmed Threshold regression asymptotics: From the compound Poisson process to two-sided Brownian motion
title_sort threshold regression asymptotics: from the compound poisson process to two-sided brownian motion
publisher Institutional Knowledge at Singapore Management University
publishDate 2018
url https://ink.library.smu.edu.sg/soe_research/2353
https://ink.library.smu.edu.sg/context/soe_research/article/3352/viewcontent/2Asys_av.pdf
https://ink.library.smu.edu.sg/context/soe_research/article/3352/filename/0/type/additional/viewcontent/2Asys_mmc1.pdf
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