| Summary: | 碩士 === 國立政治大學 === 國際貿易學系 === 83 === The Fourier transform and the wavelet transform are utilized in
this research to explore the nonlinear phenomena: the fractal
structure of long trem dependence and the phenomenon of chaos.
In terms of the two research methods of the Fourier transform
and the wavelet transform, the empirical conclusions of the
Taiwan stock exchange weighted stock index are derived as
follows: 1. The $H$ value of the research method of the Fourier
transform is 0.4632; the $H$ value of the research method of
the wavelet transform is 0.4750. The two research methods show
that the Taiwan stock market has a fractal structure of
negative long term dependence. 2. In terms of the research
method of the Fourier transform, the power spectrum of the
Taiwan stock exchange weighted stock index consists of
initially downward and wide continuous band of frequencies; the
autocorrelation function of the Taiwan stock exchange weighted
stock index decreases as the time lag increases. These
observations show that there exists the phenomenon of chaos in
the Taiwan stock market. 3. The wavelet transform can detect
out the singularities of the Taiwan stock exchange weighted
stock index and can point out the heirarchy that illustrates
the complexity of the fractal sturcture in the Taiwan stock
market. By the above empirical conclusions, there exists the
antipersistent fractal structure in the Taiwan stock market.
The variations of stock prices result from the self-similarity
of the scales of the Taiwan stock market. Even so, the
prediction of stock prices seems very impossible as a result of
the unpredictability of chaotic nature.
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