Browsing by Author "Geman, Stuart"

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Empirical scaling laws and the aggregation of non-stationary data
(2013-10-15)
Chang, Lo-Bin
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Geman, Stuart
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應用數學系
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Department of Applied Mathematics
Widely cited evidence for scaling (self-similarity) of the returns of stocks and other securities is inconsistent with virtually all currently-used models for price movements. In particular, state-of-the-art models provide for ubiquitous, irregular, and often times high-frequency fluctuations in volatility ("stochastic volatility"), both intraday and across the days, weeks, and years over which data is aggregated in demonstrations of self-similarity of returns. Stochastic volatility renders these models, which are based on variants and generalizations of random walks, incompatible with self-similarity. We show here that empirical evidence for self-similarity does not actually contradict the analytic lack of self-similarity in these models. The resolution of the mismatch between models and data can be traced to a statistical consequence of aggregating large amounts of non-stationary data. (C) 2013 The Authors. Published by Elsevier B.V. All rights reserved.
Invariance in the recurrence of large returns and the validation of models of price dynamics
(2013-08-09)
Chang, Lo-Bin
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Geman, Stuart
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Hsieh, Fushing
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Hwang, Chii-Ruey
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應用數學系
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 (Levy) random-walk models all fail to fit the statistical structure of excursions.