Applications of wavelet analysis to financial time series /
The random walk model formalized by Osbome (1964) has been the traditional model used to explain asset price behavior.Contrary to the random walk paradigm, Mandelbrot (1963) notes that financial time series have nonnormal distributions and proposes the Stable Paretian hypothesis, in which asset pric...
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
1997.
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| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=736571461&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | The random walk model formalized by Osbome (1964) has been the traditional model used to explain asset price behavior.Contrary to the random walk paradigm, Mandelbrot (1963) notes that financial time series have nonnormal distributions and proposes the Stable Paretian hypothesis, in which asset price behavior is generalized to allow the possibility of nonlinear structure. This hypothesis has received an increasing amount of empirical and theoretical support. Stable Paretian distributions are characterized by a tendency to have trends and nonlinear cycles, as well as discontinuous changes. Furthermore, observations are not usually independent; each observation carries a "memory" of all the events that precede it, and variance is typically nonstationary. In addition, such distributions are scale invariant and have fractual dimensions. Initial support for the notion that financial time series have fractal dimensions has been provided by several sources, including Hsieh (1 99 1) and Mahajan and Wagner (1 995). Many financial time series display substantial heteroskedasticity, causing difficulty in detecting trends and changes. In this study, emphasis is put on both the nonstationary character and the self-sin-similar properties of the financial time series under investigation by applying multiresolution wavelet analysis, a method developed by Mallat (I 9 89), to estimate the fractal dimension and analyze the variation of foreign exchange rates in a mixed time-scale domain. Since the fractal dimension of any deterministic system must be scale invariant, the stability of each fractal dimension estimate is tested by comparing the estimate at varying time resolutions or scales. The fractal dimension and variance estimates are used to generate simulated fractal random walks with incremental fractional Brownian motion. The distributional characteristics of simulated fractal random walk series are compared to that of traditional random walk (with incremental ordinary Browman motion) simulations, as well as sampleintraday currency exchange rate time series, to discern which diffusion process, or ordinary Brownian motion or fractional Brownian motion, more accurately describes innovations in currency exchange rates. The results of this investigation suggest that intraday currency spot exchange mte time series are not or ordinary random walks and may be more fittingly described as fractal random walks. |
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| Item Description: | Vita. "Major Subject: Finance". |
| Physical Description: | xi, 105 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references: pages 53-62. |