title: Invariance in the recurrence of large returns and the validation of models of price dynamics.
abstract: Starting from a robust, nonparametric definition of large returns ("excursions"), we study the statistics of their occurrences, focusing on the recurrence process. The empirical waiting-time distribution between excursions is remarkably invariant to year, stock, and scale (return interval). This invariance is related to self-similarity of the marginal distributions of returns, but the excursion waiting-time distribution is a function of the entire return process and not just its univariate probabilities. Generalized autoregressive conditional heteroskedasticity (GARCH) models, market-time transformations based on volume or trades, and generalized (Lévy) random-walk models all fail to fit the statistical structure of excursions.
authors.affiliation: Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan.
authors.forename: Lo-Bin
authors.initials: LB
authors.lastname: Chang
authors.forename: Stuart
authors.initials: S
authors.lastname: Geman
authors.forename: Fushing
authors.initials: F
authors.lastname: Hsieh
authors.forename: Chii-Ruey
authors.initials: CR
authors.lastname: Hwang