Semiparametric bootstrap approach to hypothesis tests and confidence intervals for the hurst coefficient - Peter Hall; Wolfgang Härdle; Torsten Kleinow; Peter Schmidt (Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, 1999)
A major application of rescaled adjusted range analysis (RS analysis) is 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 file 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 1,0 real data on commodity prices and exchange rates.
urn:nbn:de:kobv:11-10046527
Keywords: 330; Monte Carlo; box-counting method; commodity price; financial market; fractal dimension; fractional Brownian motion; Gaussian process; longrange dependence; R-S analysis; self affineness; self similarity