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Random coefficient continuous systems: testing for extreme sample path behavior

Random coefficient continuous systems: testing for extreme sample path behavior
Random coefficient continuous systems: testing for extreme sample path behavior
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 behavior according to specific regions of the parameter space that open up the potential for testing these forms of extreme behavior. 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 behavior 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 behavior. 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 1928–2018 reveals strong evidence against parameter constancy over the whole sample period leading to a long duration of what the model characterizes as extreme behavior in real stock prices.
0304-4076
208-237
Tao, Yubo
b5f501c7-fc55-4416-9866-1df230b034cb
Phillips, Peter C.B.
f67573a4-fc30-484c-ad74-4bbc797d7243
Yu, Jun
b0708df0-aac1-4595-b2fd-4c5c1aa38160
Tao, Yubo
b5f501c7-fc55-4416-9866-1df230b034cb
Phillips, Peter C.B.
f67573a4-fc30-484c-ad74-4bbc797d7243
Yu, Jun
b0708df0-aac1-4595-b2fd-4c5c1aa38160

Tao, Yubo, Phillips, Peter C.B. and Yu, Jun (2019) Random coefficient continuous systems: testing for extreme sample path behavior. Journal of Econometrics, 208-237.

Record type: Article

Abstract

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 behavior according to specific regions of the parameter space that open up the potential for testing these forms of extreme behavior. 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 behavior 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 behavior. 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 1928–2018 reveals strong evidence against parameter constancy over the whole sample period leading to a long duration of what the model characterizes as extreme behavior in real stock prices.

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Double Asymptotics for OU process in a random environment37 - Accepted Manuscript
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More information

Accepted/In Press date: 3 January 2019
e-pub ahead of print date: 18 January 2019

Identifiers

Local EPrints ID: 427353
URI: http://eprints.soton.ac.uk/id/eprint/427353
ISSN: 0304-4076
PURE UUID: 22bf0af4-9955-4d6f-b0aa-13dd833286a7
ORCID for Peter C.B. Phillips: ORCID iD orcid.org/0000-0003-2341-0451

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Date deposited: 14 Jan 2019 17:30
Last modified: 18 Feb 2021 17:14

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