Random Coefficient Continuous Systems: Testing for Extreme Sample Path Behaviour

Yubo Tao, Peter Phillips and Jun Yu

No 2114, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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 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.

Keywords: Continuous time models; Explosive path; Extreme behaviour; Random coefficient autoregression; Infill asymptotics; Bubble testing (search for similar items in EconPapers)
JEL-codes: C13 C22 G13 (search for similar items in EconPapers)
Pages: 55 pages
Date: 2017-12
New Economics Papers: this item is included in nep-ets and nep-sea
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Journal of Econometrics (April 2019), 209(2): 208-237

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Related works:
Journal Article: Random coefficient continuous systems: Testing for extreme sample path behavior (2019)
Working Paper: Random Coefficient Continuous Systems: Testing for Extreme Sample Path Behaviour (2017)
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