Abstract
• Proposing mBSDF , a modified version of backward sup df ( BSDF ) • Establishing the asymptotic theories of mBSDF • Supporting the superiority of mBSDF by empirical evidence • A meaningful supplementary for the existing empirical studies This paper considers the problem of detecting short explosive bubbles in financial data. Based on the backward sup Dickey-Fuller ( BSDF ), we propose a modified version of BSDF , namely mBSDF . We define the dating statistics by adding a modified term to the BSDF , enhancing the bubble emergence signal. We demonstrate the asymptotic distribution and the bubble duration estimates. A series of Monte Carlo simulations show that mBSDF significantly outperforms BSDF for shorter bubbles, and mBSDF can improve the bubble detection rate by up to 22 . 7%. As an empirical application, we apply the methods to the Brent crude oil futures price and the results confirm that mBSDF detects the latest oil spike shocked by the Russia-Ukraine conflict and almost all periods of explosive bubbles the oil market has experienced in recent years in contrast to BSDF , which further supports the superiority of mBSDF .
Published Version
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