Supplement to two papers on multiple bubbles [Online supplementary materials]

• Main Authors: PHILLIPS, Peter C. B., SHI, Shuping, Jun YU
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2015
• Subjects: Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2015; https://ink.library.smu.edu.sg/context/soe_research/article/3014/viewcontent/TechnicalNotes_Oct2014D.pdf
• Institution: Singapore Management University

This paper provides a supplement to two companion papers by the authors: “Testing for Multiple Bubbles: Historical Episodes of Exuberance and Collapse in the S&P 500” (PSY1 hereafter); and “Testing for Multiple Bubbles: Limit Theory of Real Time Detectors” (PSY2 hereafter). Section 1 supplements the empirical application of PSY1 by examining the robustness of the bubble identification and dating results to the choice of the minimum window size parameter used in the rolling regression framework of PSY. Section 2 provides proofs of supplementary lemmas that facilitate analysis of the multiple bubble case, derives the limit behaviour of the recursive unit root and BDF test statistics discussed in PSY2 in a model with two bubble episodes, and gives complete proofs for Theorem 4-9 in PSY2 which describe the consistency properties of the PWY, PSY and sequential PWY dating procedures.