本文選題：匯率預(yù)測(cè) + 混沌�。� 參考：《華北電力大學(xué)》2017年碩士論文

【摘要】：匯率的有效預(yù)測(cè)不但能夠影響本國(guó)與別國(guó)的經(jīng)濟(jì)與貿(mào)易,同時(shí)能夠防范國(guó)際性金融危機(jī)的發(fā)生或減少所造成的損失。傳統(tǒng)的研究方法和模型,不能夠充分的解釋匯率波動(dòng)這樣的復(fù)雜非線性系統(tǒng),混沌在非線性研究中占有重要地位,本文試圖利用混沌理論對(duì)匯率行為進(jìn)行研究,充分挖掘混沌對(duì)復(fù)雜非線性系統(tǒng)的解釋與預(yù)測(cè)能力,以期達(dá)到提高匯率預(yù)測(cè)精度的目的,以此來(lái)指導(dǎo)國(guó)家宏微觀各主體的經(jīng)濟(jì)活動(dòng)和行為。本文以混沌理論為基礎(chǔ),同時(shí)將神經(jīng)網(wǎng)絡(luò)和分形插值法應(yīng)用于匯率時(shí)間序列的研究與預(yù)測(cè)中。根據(jù)貨幣的活躍程度不同選取三個(gè)具有代表性的貨幣對(duì),美元兌人民幣、英鎊兌人民幣、加元兌人民幣。首先,借助于圖示法和指標(biāo)法對(duì)其進(jìn)行統(tǒng)計(jì)性描述,并進(jìn)行非線性特征分析。然后,利用C-C算法求得三個(gè)匯率時(shí)間序列的時(shí)間延遲、嵌入維數(shù)以此來(lái)重構(gòu)相空間,在此基礎(chǔ)之上,利用wolf算法和G-P算法分別求出最大Lyapunov指數(shù)和分形維數(shù),對(duì)匯率的混沌特性進(jìn)行驗(yàn)證。在確定匯率系統(tǒng)的混沌性之后,根據(jù)匯率的混沌特征來(lái)分別建立神經(jīng)網(wǎng)絡(luò)和分形插值預(yù)測(cè)模型。神經(jīng)網(wǎng)絡(luò)的構(gòu)建是將混沌系統(tǒng)重構(gòu)相空間的最佳嵌入維作為輸入層的神經(jīng)元數(shù),并將重構(gòu)相空間中的時(shí)序向量作為神經(jīng)元的輸入量;分形插值模型中的垂直比例因子則根據(jù)分形維數(shù)計(jì)算求得。最后,在分別利用兩個(gè)模型進(jìn)行預(yù)測(cè)的基礎(chǔ)上,根據(jù)較大誤差在組合預(yù)測(cè)模型中占比較小的原則進(jìn)行動(dòng)態(tài)組合預(yù)測(cè)的實(shí)證研究。本文通過對(duì)三個(gè)人民幣匯率的統(tǒng)計(jì)性描述得出,匯率時(shí)間序列不服從正態(tài)分布,具有非線性特征。同時(shí),求得的三個(gè)最大Lyapunov指數(shù)都為正數(shù),而分形維數(shù)都為較小的分?jǐn)?shù),這表明三個(gè)匯率序列都為對(duì)初始條件都具有敏感性的低維混沌系統(tǒng)。以混沌理論為基礎(chǔ)的匯率組合預(yù)測(cè)模型在有效利用混沌對(duì)復(fù)雜系統(tǒng)解釋能力的同時(shí),能將神經(jīng)網(wǎng)絡(luò)的非線性逼近能力以及分形插值對(duì)不光滑曲線的擬合能力結(jié)合應(yīng)用。預(yù)測(cè)結(jié)果表明,組合預(yù)測(cè)模型能夠保留單個(gè)預(yù)測(cè)模型的優(yōu)勢(shì)的同時(shí)降低單個(gè)模型的缺點(diǎn)在預(yù)測(cè)中的影響,預(yù)測(cè)精度得到有效提高。
[Abstract]:The effective prediction of exchange rate can not only affect the economy and trade between our country and other countries, but also prevent the loss caused by the international financial crisis. Traditional research methods and models can not fully explain the complex nonlinear system such as exchange rate fluctuations. Chaos plays an important role in nonlinear research. This paper attempts to use chaos theory to study exchange rate behavior. In order to improve the accuracy of exchange rate prediction, the chaotic interpretation and prediction ability of complex nonlinear systems can be fully exploited to guide the economic activities and behaviors of the national macro and micro entities. In this paper, based on chaos theory, neural network and fractal interpolation are applied to the study and prediction of exchange rate time series. Three representative pairs, the dollar versus the renminbi, the pound against the renminbi and the Canadian dollar against the yuan, are chosen depending on the currency's activity. Firstly, the statistical description and nonlinear characteristic analysis are carried out with the help of graphical method and index method. Then, the time delay of three exchange rate time series is obtained by C-C algorithm, and the embedded dimension is used to reconstruct the phase space. On this basis, the maximum Lyapunov exponent and fractal dimension are obtained by using wolf algorithm and G-P algorithm, respectively. The chaos characteristic of exchange rate is verified. After the chaos of exchange rate system is determined, neural network and fractal interpolation prediction model are established according to the chaotic characteristics of exchange rate. The optimal embedding dimension of the reconstructed phase space of the chaotic system is taken as the number of neurons in the input layer, and the time series vector in the reconstructed phase space is taken as the input quantity of the neuron. The vertical scaling factor in the fractal interpolation model is calculated according to the fractal dimension. Finally, on the basis of the two models, the dynamic combination prediction is studied based on the principle that the large error is small in the combination forecasting model. Based on the statistical description of the three RMB exchange rates, it is concluded that the time series of exchange rates are not obedient to normal distribution and have nonlinear characteristics. At the same time, the three largest Lyapunov exponents obtained are all positive numbers, while the fractal dimensions are all small fractions, which indicates that the three exchange rate sequences are all low-dimensional chaotic systems with sensitivity to initial conditions. The exchange rate combination forecasting model based on chaos theory can effectively utilize the ability of chaotic interpretation to complex system, at the same time, it can combine the nonlinear approximation ability of neural network and the ability of fractal interpolation to fit the non-smooth curve. The prediction results show that the combined prediction model can preserve the advantages of the single prediction model and reduce the influence of the shortcomings of the single model in the prediction, and the prediction accuracy is improved effectively.
【學(xué)位授予單位】：華北電力大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP183;F832.6;F224

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本文編號(hào)：1975890