Testing for Multiple Bubbles: Limit Theory of Real Time Detectors

Peter Phillips, Shuping Shi and Jun Yu

No 1915, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper provides the limit theory of real time dating algorithms for bubble detection that were suggested in Phillips, Wu and Yu (2011, PWY) and Phillips, Shi and Yu (2013b, PSY). Bubbles are modeled using mildly explosive bubble episodes that are embedded within longer periods where the data evolves as a stochastic trend, thereby capturing normal market behavior as well as exuberance and collapse. Both the PWY and PSY estimates rely on recursive right tailed unit root tests (each with a different recursive algorithm) that may be used in real time to locate the origination and collapse dates of bubbles. Under certain explicit conditions, the moving window detector of PSY is shown to be a consistent dating algorithm even in the presence of multiple bubbles. The other algorithms are consistent detectors for bubbles early in the sample and, under stronger conditions, for subsequent bubbles in some cases. These asymptotic results and accompanying simulations guide the practical implementation of the procedures. They indicate that the PSY moving window detector is more reliable than the PWY strategy, sequential application of the PWY procedure and the CUSUM procedure.

Keywords: Bubble duration; Consistency; Dating algorithm; Limit theory; Multiple bubbles; Real time detector (search for similar items in EconPapers)
JEL-codes: C15 C22 (search for similar items in EconPapers)
Pages: 75 pages
Date: 2013-09
New Economics Papers: this item is included in nep-cmp, nep-ets and nep-sea
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Published in International Economic Review (November 2015), 56(4): 1079-1134

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Related works:
Journal Article: TESTING FOR MULTIPLE BUBBLES: LIMIT THEORY OF REAL‐TIME DETECTORS (2015)
Working Paper: Testing for Multiple Bubbles 2: Limit Theory of Real Time Detectors (2013)
Working Paper: Testing for Multiple Bubbles 2: Limit Theory of Real Time Detectors (2013)
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