We consider the role of finite size effects on the value of the effective Hurst exponent H. This problem is motivated by the properties of the high-frequency daily stock-prices. For a finite size random walk we derive some exact results based on Spitzer's identity. The conclusion is that finite size effects strongly enhance the value of H and the convergency to the asymptotic value (H = (1)/(2)) is rather slow. This result has a series of conceptual and practical implication which we discuss. (c) 2006 Elsevier B.V. All rights reserved.
Exact results for the roughness of a finite size random walk
Coccetti F;
2006-01-01
Abstract
We consider the role of finite size effects on the value of the effective Hurst exponent H. This problem is motivated by the properties of the high-frequency daily stock-prices. For a finite size random walk we derive some exact results based on Spitzer's identity. The conclusion is that finite size effects strongly enhance the value of H and the convergency to the asymptotic value (H = (1)/(2)) is rather slow. This result has a series of conceptual and practical implication which we discuss. (c) 2006 Elsevier B.V. All rights reserved.File in questo prodotto:
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