Empirical scaling laws and the aggregation of non-stationary data

Lo-Bin Chang and Stuart Geman

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 20, 5046-5052

Abstract: 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 oftentimes 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.

Keywords: Random-walk models; Self-similarity; Stochastic volatility; Market time (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:20:p:5046-5052

DOI: 10.1016/j.physa.2013.06.049

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