本文選題：非線性 + 分形��； 參考：《中國海洋大學》2013年碩士論文

【摘要】：作為現(xiàn)代金融研究的理論基礎，有效市場假說無法很好地解釋市場行為，假設條件也與實際經驗不符，這時，非線性科學中的新分支——分形理論應運而生。運用分形理論分析非線性系統(tǒng)中不規(guī)則或者不光滑個體，能夠較好地解釋復雜性系統(tǒng)的特征和行為。集貨幣、金融、商品屬性于一身的黃金近幾年一直是國內外投資者和避險者紛紛追逐的對象，黃金市場行為和價格波動也逐漸受到廣泛關注�？紤]到有效市場理論在分析金融市場時的缺陷，本文借助非線性方法和理論認識我國黃金現(xiàn)貨市場、研究我國黃金現(xiàn)貨市場波動特征和行為、預測黃金市場價格具有重要的意義和價值。本文的研究工作主要集中在以下幾個方面： 首先，分析了有效市場假說在解釋市場現(xiàn)象中存在的局限和不足，即市場上的參與者并不是完全理性的、收益率不遵循隨機游走以及市場價格對信息的非線性反應等，介紹了具有更廣泛適用性的分形市場假說，系統(tǒng)地梳理了分形理論和相應的分析方法，分析了研究非線性和復雜系統(tǒng)的分形理論在黃金市場上的應用。 其次，判斷了數(shù)據(jù)的平穩(wěn)性并對其進行平穩(wěn)化處理，對處理后的收益率序列進行正態(tài)性檢驗、線性檢驗、非線性檢驗、R/S分析以及盒子覆蓋法分析。研究工作主要有：1）通過ADF、PP等方法綜合判斷了數(shù)據(jù)的平穩(wěn)性，對收益率平穩(wěn)化處理后的數(shù)據(jù)進行正態(tài)性檢驗、線性相關檢驗和非線性相關檢驗。2）運用重標極差分析法計算黃金日收益率和周收益率序列的Hurst指數(shù)，實證結果說明黃金市場是分形的，時間序列存在長期記憶性，并且有112天的非周期循環(huán)長度。3）用盒子覆蓋法計算時間序列的盒維數(shù)，得到的盒維非整數(shù)，與前文分析一同從整體上說明了我國黃金現(xiàn)貨市場的分形特征。 再次，運用多重分形方法繼續(xù)深入研究黃金現(xiàn)貨市場的多重分形特征及其影響因素、原因。研究工作主要有：1）運用多重分形消除趨勢波動分析法計算黃金時間序列的廣義Hurst指數(shù)、標度函數(shù)、奇異指數(shù)、多重分形譜，結果說明時間序列在消除趨勢后，局部結構不一致，存在多重分形特征。2）通過相位隨機化和打亂處理，對比原序列和新序列的分形特征，分析影響多重分形的因素。3）分析市場內出現(xiàn)分形結構的原因。 最后，，在實證檢驗了我國黃金現(xiàn)貨市場的長期記憶性和標度不變性等分形特征之后，構建分形插值模型，擬合分形插值曲線，并對我國黃金現(xiàn)貨市場價格進行預測，為市場投資者和管理者認識市場、預測市場提供了參考。
[Abstract]:As the theoretical basis of modern financial research, the efficient market hypothesis can not explain market behavior well, and the hypothetical conditions are not consistent with practical experience. At this time, a new branch of nonlinear science-fractal theory emerges as the times require. Using fractal theory to analyze irregular or non-smooth individuals in nonlinear systems can better explain the characteristics and behaviors of complex systems. In recent years, gold, which has the property of currency, finance and commodity, has been pursued by investors at home and abroad, and the behavior and price fluctuation of gold market have been paid more and more attention. Considering the defects of the efficient market theory in analyzing the financial market, this paper studies the fluctuation characteristics and behavior of China's gold spot market by means of nonlinear methods and theories. Forecasting gold market price has important meaning and value. The research work of this paper mainly focuses on the following aspects: Firstly, the limitations and shortcomings of the efficient market hypothesis in explaining the market phenomenon are analyzed, that is, the participants in the market are not completely rational, the rate of return does not follow the random walk and the nonlinear response of the market price to the information, etc. This paper introduces the fractal market hypothesis which has more extensive applicability, systematically combs the fractal theory and the corresponding analysis methods, and analyzes the application of fractal theory to the gold market for the study of nonlinear and complex systems. Secondly, the smoothness of the data is judged and processed, the normality test, the linear test, the nonlinear test and the box coverage analysis are carried out. The research work mainly includes: (1) judging the stability of the data synthetically through ADFU PP and so on, and testing the normality of the data after the rate of return is stabilized. Linear correlation test and nonlinear correlation test. 2) the Hurst index of gold daily yield and weekly rate of return is calculated by the method of rescaled range. The empirical results show that the gold market is fractal, and the time series have long-term memory. And there are 112 days of aperiodic cycle length. 3) the box dimension of the time series is calculated by the box covering method, and the box dimension is not an integer. Together with the previous analysis, the fractal characteristics of the gold spot market in our country are explained as a whole. Thirdly, multifractal method is used to study the multifractal characteristics of gold spot market and its influencing factors. The main research work is: (1) the generalized Hurst exponent, scale function, singular index, multifractal spectrum of prime time series are calculated by multifractal elimination trend fluctuation analysis method. The results show that the local structure of time series is inconsistent after eliminating the trend. There are multifractal features. 2) by phase randomization and scrambling processing, comparing the fractal characteristics of the original sequence with the new sequence, and analyzing the factors affecting multifractal. 3) analyzing the reason of the fractal structure in the market. Finally, after testing the long-term memory and scale invariance of China's gold spot market, a fractal interpolation model is constructed to fit the fractal interpolation curve, and the gold spot market price in China is forecasted. It provides a reference for market investors and managers to understand the market and forecast the market.
【學位授予單位】：中國海洋大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：F832.54

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