Random coefficient continuous systems: Testing for extreme sample path behaviour

This paper studies a continuous time dynamic system with a random persistence parameter. The exact discrete time representation is obtained and related to several discrete time random coefficient models currently in the literature. The model distinguishes various forms of unstable and explosive beha...

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Main Authors: TAO, Yubo, PHILLIPS, Peter C. B., YU, Jun
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Language:English
Published: Institutional Knowledge at Singapore Management University 2017
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Online Access:https://ink.library.smu.edu.sg/soe_research/2115
https://ink.library.smu.edu.sg/context/soe_research/article/3115/viewcontent/Double_Asymptotics_for_OU_process_in_a_random_environment19_.pdf
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spelling sg-smu-ink.soe_research-31152017-12-15T07:01:58Z Random coefficient continuous systems: Testing for extreme sample path behaviour TAO, Yubo PHILLIPS, Peter C. B. YU, Jun This paper studies a continuous time dynamic system with a random persistence parameter. The exact discrete time representation is obtained and related to several discrete time random coefficient models currently in the literature. The model distinguishes various forms of unstable and explosive behaviour according to specific regions of the parameter space that open up the potential for testing these forms of extreme behaviour. A two-stage approach that employs realized volatility is proposed for the continuous system estimation, asymptotic theory is developed, and test statistics to identify the different forms of extreme sample path behaviour are proposed. Simulations show that the proposed estimators work well in empirically realistic settings and that the tests have good size and power properties in discriminating characteristics in the data that differ from typical unit root behaviour. The theory is extended to cover models where the random persistence parameter is endogenously determined. An empirical application based on daily real S&P 500 index data over 1964-2015 reveals strong evidence against parameter constancy after early 1980, which strengthens after July 1997, leading to a long duration of what the model characterizes as extreme behaviour in real stock prices. 2017-11-01T07:00:00Z text application/pdf https://ink.library.smu.edu.sg/soe_research/2115 https://ink.library.smu.edu.sg/context/soe_research/article/3115/viewcontent/Double_Asymptotics_for_OU_process_in_a_random_environment19_.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Economics eng Institutional Knowledge at Singapore Management University Continuous time models Explosive path Extreme behaviour; Random coefficient autoregression; Infill asymptotics; Bubble testing. Econometrics
institution Singapore Management University
building SMU Libraries
continent Asia
country Singapore
Singapore
content_provider SMU Libraries
collection InK@SMU
language English
topic Continuous time models
Explosive path
Extreme behaviour; Random coefficient autoregression; Infill asymptotics; Bubble testing.
Econometrics
spellingShingle Continuous time models
Explosive path
Extreme behaviour; Random coefficient autoregression; Infill asymptotics; Bubble testing.
Econometrics
TAO, Yubo
PHILLIPS, Peter C. B.
YU, Jun
Random coefficient continuous systems: Testing for extreme sample path behaviour
description This paper studies a continuous time dynamic system with a random persistence parameter. The exact discrete time representation is obtained and related to several discrete time random coefficient models currently in the literature. The model distinguishes various forms of unstable and explosive behaviour according to specific regions of the parameter space that open up the potential for testing these forms of extreme behaviour. A two-stage approach that employs realized volatility is proposed for the continuous system estimation, asymptotic theory is developed, and test statistics to identify the different forms of extreme sample path behaviour are proposed. Simulations show that the proposed estimators work well in empirically realistic settings and that the tests have good size and power properties in discriminating characteristics in the data that differ from typical unit root behaviour. The theory is extended to cover models where the random persistence parameter is endogenously determined. An empirical application based on daily real S&P 500 index data over 1964-2015 reveals strong evidence against parameter constancy after early 1980, which strengthens after July 1997, leading to a long duration of what the model characterizes as extreme behaviour in real stock prices.
format text
author TAO, Yubo
PHILLIPS, Peter C. B.
YU, Jun
author_facet TAO, Yubo
PHILLIPS, Peter C. B.
YU, Jun
author_sort TAO, Yubo
title Random coefficient continuous systems: Testing for extreme sample path behaviour
title_short Random coefficient continuous systems: Testing for extreme sample path behaviour
title_full Random coefficient continuous systems: Testing for extreme sample path behaviour
title_fullStr Random coefficient continuous systems: Testing for extreme sample path behaviour
title_full_unstemmed Random coefficient continuous systems: Testing for extreme sample path behaviour
title_sort random coefficient continuous systems: testing for extreme sample path behaviour
publisher Institutional Knowledge at Singapore Management University
publishDate 2017
url https://ink.library.smu.edu.sg/soe_research/2115
https://ink.library.smu.edu.sg/context/soe_research/article/3115/viewcontent/Double_Asymptotics_for_OU_process_in_a_random_environment19_.pdf
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