This paper addresses the statistical properties of time series driven by rational bubbles a la Blanchard and Watson (1982). Using insights on the behavior of multiplicative stochastic processes, we demonstrate that the tails of the unconditional distribution emerging from such bubble processes...

By combining (i) the economic theory of rational expectation bubbles, (ii) behavioral finance on imitation and herding of investors and traders and (iii) the mathematical and statistical physics of bifurcations and phase transitions, the log-periodic power law (LPPL) model has been developed as...

We present the symmetric thermal optimal path (TOPS) method to determine the time-dependent lead-lag relationship between two stochastic time series. This novel version of the previously introduced TOP method alleviates some inconsistencies by imposing that the lead-lag relationship should be...

Cover -- Title -- Copyright -- Contents -- Preface to the Princeton Science Library Edition -- Preface to the 2002 Edition -- Chapter 1 FINANCIAL CRASHES: WHAT, HOW, WHY, AND WHEN? -- What Are Crashes, and Why Do We Care? -- The Crash of October 1987 -- Historical Crashes -- The Tulip Mania --...