| dc.contributor.advisor | 胡聯國 | zh_TW |
| dc.contributor.advisor | Hu, Len Kuo | en_US |
| dc.contributor.author (Authors) | 陳國帥 | zh_TW |
| dc.contributor.author (Authors) | Chen, Kuo Shuai | en_US |
| dc.creator (作者) | 陳國帥 | zh_TW |
| dc.creator (作者) | Chen, Kuo Shuai | en_US |
| dc.date (日期) | 1994 | en_US |
| dc.date.accessioned | 29-Apr-2016 09:15:25 (UTC+8) | - |
| dc.date.available | 29-Apr-2016 09:15:25 (UTC+8) | - |
| dc.date.issued (上傳時間) | 29-Apr-2016 09:15:25 (UTC+8) | - |
| dc.identifier (Other Identifiers) | B2002003378 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/87853 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 國際經營與貿易學系 | zh_TW |
| dc.description (描述) | G82351031 | zh_TW |
| dc.description.abstract (摘要) | 本文採用傅利葉轉換與小波轉換以探討非線性現象：長期相依的碎形結構與混沌現象。藉由傅利葉轉換與小波轉換兩種研究方法，所得到臺灣股票市場加權股價指數的實證結論如下：1.藉由傅利葉轉換所得到的H值為0.4632；藉由小波轉換所得到的H值為0.4750。這兩種研究方法皆顯示臺灣股票市場具有負的長期相依的碎形結構。2.藉由傅利葉轉換的研究方法，臺灣股票市場加權股價指數的頻譜由初始向下與寬的連續的頻帶所組成；臺灣股票市場加權股價指數的自我相關函數則隨著時間差距的增加而遞減。此顯示臺灣股票市場具有混沌現象。3.小波轉換可以檢測出臺灣股票市場加權股價指數的奇異之處，並且指出存有一能說明臺灣股票市場碎形結構的複雜性的機制。藉由以上的實證結論，可以得知臺灣股票市場具有反持續性的碎形結構，股票價格的變動來自於臺灣股票市場尺度上的自我相似性。即使如此，由於混沌不可預測性的本質，使得股票價格的預測似乎是不可能的。 | zh_TW |
| dc.description.abstract (摘要) | 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. | en_US |
| dc.description.tableofcontents | 謝辭 Abstract Contents-----i List of Figures-----iii List of Tables-----vi 1 Introduction-----1 1.1 Motivation of Research-----1 1.2 Purposes of Research-----1 1.3 Scope of Research-----3 1.4 Structure of Research-----3 2 Review of Literature-----4 2.1 Fractional Brownian Motion and Fractal Structure-----4 2.2 Introduction to Fractals-----9 2.3 Introduction to Chaos-----11 3 Research Method (I) Fourier Transform-----18 3.1 Fourier Series-----18 3.2 Fourier Transform-----23 3.3 Fourier Transform and Fractional Brownian Motion-----27 3.4 Fourier Transform and Chaotic Signals-----30 4 Research Method (II) Wavelet Transform-----36 4.1 Wavelet Transform-----36 4.2 Comparison between Fourier Transform and Wavelet Transform-----45 4.3 Wavelet Transform and Fractional Brownian Motion-----47 4.4 Wavelet Transform and Fractallike Signals-----48 5 Empirical Results and Analyses-----53 5.1 Empirical Studies of Fourier Transform-----53 5.1.1 Empirical Analysis of Fractal Structure-----55 5.1.2 Empirical Analysis of Chaos-----57 5.2 Empirical Studies of Wavelet Transform-----59 5.2.1 Empirical Analysis of Fractal Structure-----60 5.2.2 Empirical Analysis of Fractallike Data-----64 5.3 Empirical Conclusions-----72 6 Conclusions and Suggestions-----73 6.1 Conclusions of Research-----73 6.2 Suggestions of Research-----74 List of Figures 2.1 Cantor ternary set. Data resource: Gulick (1992), pp.192-----9 2.2 von Koch curve. Data resource: Gulick (1992), pp.195-----10 3.1 The relationship between data, Fourier transform, power spectrum and autocorrelation function. Data resource: This research-----26 3.2 Four attractors: (a), point attractor, (b). limit cycle,(c). torus, (d). strange attractor. Date resource: Gulick (1987), pp-50-----33 3.3 Point attractor. Data resource: Argyris, Faust and Haase (1994), pp.149-----33 3.4 Limit cycle. Data resource: Argyris, Faust and Haase (1994), pp.149-----34 3.5 Torus. Data resource: Argyris, Faust and Haase (1994), pp.149-----34 3.6 Strange attractor. Data resource: Argyris, Faust and Haase (1994), pp.149-----35 3.7 White noise. Data resource: Argyris, Faust and Haase (1994), pp.149-----35 4.1 The comparison between Fourier transform and wavelet transform. (a) Fourier transform. Perfect wavenumber-space resolution, no physical-space resolution, (b) Wavelet transform. Balance between wavenumber- and physical-space resolution varies with length-scale. Smaller length-scales are more finely resolved: mathematical microscope. Data resource: Farge, Hunt and Vassilicos (1993), pp.19-----38 4.2 Flexible time-frequency windows, a1 < a2. Data resource: Chui (1992), pp.9-----40 4.3 Haar wavelet. Data resource: Wei (1994)-----42 4.4 Hat wavelet. Data resource: Wei (1994)-----43 4.5 Mexican hat wavelet. Data resource: Wei (1994)-----43 4.6 Gaussian wavelet. Data resource: Wei (1994)-----44 4.7 Morlet wavelet. Data resource: Wei (1994)-----44 4.8 The question of singular points. Data resource: This research-----45. 4.9 The wavelet transform of the Cantor ternary set. Data resource: Argoul et al. (1989)-----50 4.10 The construction rule of the Cantor ternary set. Data resource: Argoul et al. (1989)-----51 4.11 The wavelet analysis of the wind tunnel data. The top graphs show the signal being analyzed, (a), the wavelet transform of a 852 m-long sample from the scale 28 lo to the scale lo/10; (b). magnification x20 of the central position indicated by the arrow in the top graph of (a); (c). magnification x20 of the central position indicated by the arrow in the top graph of (b).Data resource: Argoul et al. (1989)-----52 5.1 The Taiwan stock exchange weighted stock index. Data resource: This research-----54 5.2 The original power spectrum of the Taiwan stock exchange weighted stock index. Data resource: This research-----55 5.3 The power spectrum of the Taiwan stock exchange weighted stock index. Data resource: This research-----56 5.4 The log-log plot of the power spectrum versus frequency. Data resource: This research-----57 5.5 The autocorrelation function of the Taiwan stock exchange weighted stock index. Data resource: This research-----58 5.6 The orthonormal Maxican hat wavelet. Data resource: Wei (1994)-----59 5.7 The wavelet transform of the Taiwan stock exchange weighted stock index of 4096 trading days. Data resource: This research-----65 5.8 The contour map of the wavelet transform of the Taiwan stock exchange weighted stock index of 4096 trading days. Data resource: This research-----66 5.9 The Taiwan stock exchange weighted stock index between the 2000th and the 3000th trading days. Data resource: This research-----69 5.10 The wavelet transform of the Taiwan stock exchange weighted stock index between the 2000th and the 3000th trading days. Data resource: This research-----70 5.11 The contour map of the wavelet transform of the Taiwan stock exchange weighted stock index between the 2000th and the 3000th trading days. Data resource: This research-----71 List of Tables 5.1 The wavelet coefficients of the Taiwan stock exchange weighted stock index of 4096 trading days. Data resource: This research-----62 5.2 The wavelet coefficients of the Taiwan stock exchange weighted stock index between the 2000th and the 3000th trading days. Data resource: This research-----67 | zh_TW |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#B2002003378 | en_US |
| dc.subject (關鍵詞) | 非線性 | zh_TW |
| dc.subject (關鍵詞) | 碎形結構 | zh_TW |
| dc.subject (關鍵詞) | 混沌 | zh_TW |
| dc.subject (關鍵詞) | 傅利葉轉換 | zh_TW |
| dc.subject (關鍵詞) | 小波轉換 | zh_TW |
| dc.subject (關鍵詞) | 臺灣股票市場 | zh_TW |
| dc.subject (關鍵詞) | Nonlinear | en_US |
| dc.subject (關鍵詞) | Fractal Structure | en_US |
| dc.subject (關鍵詞) | Chaos | en_US |
| dc.subject (關鍵詞) | Fourier Transform | en_US |
| dc.subject (關鍵詞) | Wavelet Transform | en_US |
| dc.subject (關鍵詞) | Taiwan Stock Market | en_US |
| dc.title (題名) | 臺灣股票市場非線性現象之研究：傅利葉轉換與小波轉換之應用 | zh_TW |
| dc.title (題名) | The Research of Nonlinear Phenomena of the Taiwan Stock Market: the Applications of Fourier Transform and Wavelet Transform | en_US |
| dc.type (資料類型) | thesis | en_US |
