Fractal market time
AbstractAné and Geman (2000) observed that market returns appear to follow a conditional Gaussian distribution where the conditioning is a stochastic clock based on cumulative transaction count. The existence of long range dependence in the squared and absolute value of market returns is a ‘stylized fact’ and researchers have interpreted this to imply that the stochastic clock is self-similar, multi-fractal (Mandelbrot, Fisher and Calvet, 1997) or mono-fractal (Heyde, 1999). We model the market stochastic clock as the stochastic integrated intensity of a doubly stochastic Poisson (Cox) point process of the cumulative transaction count of stocks traded on the New York Stock Exchange (NYSE). A comparative empirical analysis of a self-normalized version of the stochastic integrated intensity is consistent with a mono-fractal market clock with a Hurst exponent of 0.75.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Empirical Finance.
Volume (Year): 19 (2012)
Issue (Month): 5 ()
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Web page: http://www.elsevier.com/locate/jempfin
Market time deformation; Long range dependent; Stochastic clock; Fractal Activity Time; Doubly stochastic binomial point process;
Find related papers by JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
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