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Empirically based modeling in financial economics and beyond, and spurious stylized facts

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Author Info
Bassler, Kevin E.
Gunaratne, Gemunu H.
McCauley, Joseph L.
Abstract

The discovery of the dynamics of a time series requires construction of the transition density. We explain why 1-point densities and scaling exponents cannot determine the class of stochastic dynamics. Time series require some sort of underlying statistical regularity to provide a basis for analysis, and we construct an exhaustive list of such tests. The condition for stationary increments, not scaling, determines the existence of long time pair autocorrelations. We conjecture that for a selfsimilar process neither the pair correlations nor the 2-point density scales in both times t and s except in a pathological case, and give examples using three well-known Gaussian processes. An incorrect assumption of stationary increments can generate spurious stylized facts, including fat tails. When a sliding window is applied to nonstationary, uncorrelated increments then a Hurst exponent Hs = 1 / 2 is generated by that procedure even if the underlying model scales with a Hurst exponent H [not equal to] 1/2. We explain how this occurs dynamically. The nonstationarity arises from systematic unevenness in the traders' behavior in real time. Spurious stylized facts arise mathematically from using a log increment with a [`]sliding window' to read the series. In addition, we show that nonstationary processes are generally not globally transformable to stationary ones. We also present a more detailed explanation of our recent FX data analysis and modeling.

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Publisher Info
Article provided by Elsevier in its journal International Review of Financial Analysis.

Volume (Year): 17 (2008)
Issue (Month): 5 (December)
Pages: 767-783
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:eee:finana:v:17:y:2008:i:5:p:767-783

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Web page: http://www.elsevier.com/locate/inca/620166

For technical questions regarding this item, or to correct its listing, contact: (Heidi Boesdal).

Related research
Keywords: Nonstationary differences Scaling Fat tails FX analysis Martingales Volatility Stylized facts;

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