Invariance in the recurrence of large returns and the validation of models of price dynamics
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An R-Based Landscape Validation of a Competing Risk Model
Published on: September 16, 2022
Lo-Bin Chang1, Stuart Geman, Fushing Hsieh
1Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan.
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.
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