Semiparametric Bootstrap Approach to Hypothesis Tests and Confidence Intervals for the Hurst Coefficient |
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Authors: | Hall Peter Härdle Wolfgang Kleinow Torsten Schmidt Peter |
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Institution: | 1.Centre for Mathematics and its Applications, Australian National University, Canberra, ACT, 0200, Australia ;2.Institut für Statistik und ?konometrie, Humboldt-Universit?t zu Berlin, Spandauer Str. 1, D–10178, Berlin, Germany ;3.Quantitative Research, Bankgesellschaft Berlin AG, Germany ; |
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Abstract: | A major application of rescaled adjusted range analysis (R–S analysis) is to the study of price fluctuations in financial
markets. There, the value of the Hurst constant, H, in a time series may be interpreted as an indicator of the irregularity of the price of a commodity, currency or similar
quantity. Interval estimation and hypothesis testing for H are central to comparative quantitative analysis. In this paper we propose a new bootstrap, or Monte Carlo, approach to such
problems. Traditional bootstrap methods in this context are based on fitting a process chosen from a wide but relatively conventional
range of discrete time series models, including autoregressions, moving averages, autoregressive moving averages and many
more. By way of contrast we suggest simulation using a single type of continuous-time process, with its fractal dimension.
We provide theoretical justification for this method, and explore its numerical properties and statistical performance by
application to real data on commodity prices and exchange rates.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | Box-counting method commodity price financial market fractal dimension fractional Brownian motion Gaussian process long-range dependence Monte Carlo R– S analysis self affineness self similarity |
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