本文選題：動(dòng)力學(xué)模型 + 多維泰勒網(wǎng)　； 參考：《東南大學(xué)》2014年博士論文

【摘要】：金融系統(tǒng)是市場(chǎng)經(jīng)濟(jì)中市場(chǎng)資源合理配置機(jī)制的主導(dǎo)與樞紐,金融系統(tǒng)的正常運(yùn)行是保證國(guó)家經(jīng)濟(jì)運(yùn)行穩(wěn)定的必要條件。金融數(shù)據(jù)包括股票價(jià)格,存貸款,基金,保險(xiǎn)和外匯等,是經(jīng)濟(jì)數(shù)據(jù)中最重要的數(shù)據(jù)類型。對(duì)金融數(shù)據(jù)進(jìn)行研究、分析和預(yù)測(cè)可以為國(guó)家宏觀調(diào)控的制定做出指導(dǎo)方針。建立金融系統(tǒng)數(shù)學(xué)模型是研究金融系統(tǒng)的主要途徑�，F(xiàn)有基于金融系統(tǒng)運(yùn)行機(jī)理的模型,主要針對(duì)具體金融領(lǐng)域展開,用以解決具體問題,但因金融系統(tǒng)結(jié)構(gòu)復(fù)雜易變而存在局限性�；诜菣C(jī)理的數(shù)據(jù)建模方法,通過計(jì)算機(jī)的高速運(yùn)轉(zhuǎn),可以快速處理大量金融數(shù)據(jù),在金融數(shù)據(jù)分析中得到更廣泛的應(yīng)用,但是其存在僅關(guān)注數(shù)據(jù)內(nèi)在聯(lián)系而脫離實(shí)際的問題。為了建立更好的金融模型,使其為經(jīng)濟(jì)控制和國(guó)家宏觀調(diào)控研究奠定基礎(chǔ),本文提出了基于多維泰勒網(wǎng)(MTN)的金融數(shù)據(jù)建模和預(yù)測(cè)方法,并進(jìn)一步提出基于其擴(kuò)展的動(dòng)力學(xué)特性聚類多維泰勒網(wǎng)(DCMTN)、間歇反饋多維泰勒網(wǎng)(IFB-MTN)和帶間歇反饋的多重多維泰勒網(wǎng)(MIMTN)金融數(shù)據(jù)建模和預(yù)測(cè)方法。本文以金融系統(tǒng)數(shù)據(jù)建模為背景,針對(duì)不同的建模側(cè)重點(diǎn),提出了數(shù)學(xué)模型,給出了相應(yīng)模型求解方法。論文主要工作概括如下：1.針對(duì)金融系統(tǒng)內(nèi)部要素多,結(jié)構(gòu)復(fù)雜的問題,建立基于數(shù)據(jù)的金融系統(tǒng)動(dòng)力學(xué)模型。研究了一般動(dòng)力學(xué)模型的形式,結(jié)合金融系統(tǒng)含有多維狀態(tài)向量的特點(diǎn)和泰勒展開式的基本原理,提出了多維泰勒網(wǎng)動(dòng)力學(xué)模型。證明了多維泰勒網(wǎng)模型表達(dá)式的合理性,明確了模型中加權(quán)項(xiàng)排列次序和遞歸表達(dá)式。通過共軛梯度法對(duì)模型參數(shù)的迭代求解,得到了多維泰勒網(wǎng)模型參數(shù)求解的一般方法。為了測(cè)試模型的有效性,先通過數(shù)據(jù)濾波和分解方法,減少金融數(shù)據(jù)中隨機(jī)擾動(dòng)帶來的影響,然后對(duì)分解后的每個(gè)數(shù)據(jù)子集分別建立多維泰勒網(wǎng)模型、辨識(shí)其參數(shù)并進(jìn)行預(yù)測(cè),最后將預(yù)測(cè)結(jié)果疊加輸出。仿真實(shí)驗(yàn)結(jié)果表明了模型及算法的有效性,也為基于多維泰勒網(wǎng)模型的擴(kuò)展研究奠定基礎(chǔ)。2.針對(duì)金融系統(tǒng)內(nèi)部流動(dòng)性快,結(jié)構(gòu)和特性易變的特點(diǎn),建立動(dòng)力學(xué)特性隨預(yù)測(cè)目標(biāo)不同而改變的金融系統(tǒng)動(dòng)力學(xué)預(yù)測(cè)模型。研究了金融系統(tǒng)的動(dòng)力學(xué)特點(diǎn),定義了動(dòng)力學(xué)特性,并證明了其數(shù)學(xué)表達(dá)形式的合理性。根據(jù)金融數(shù)據(jù)中數(shù)據(jù)點(diǎn)的不同動(dòng)力學(xué)特性相似程度,定義了動(dòng)力學(xué)特性相似度的具體形式,總結(jié)歸納并證明了其擁有的性質(zhì)。結(jié)合多維泰勒網(wǎng)和動(dòng)力學(xué)特性及相似度,提出了基于動(dòng)力學(xué)特性聚類多維泰勒網(wǎng)的金融系統(tǒng)動(dòng)力學(xué)預(yù)測(cè)模型。通過最小二乘估計(jì)的方法辨識(shí)了模型的參數(shù)。實(shí)例結(jié)果表明,動(dòng)力學(xué)特性聚類多維泰勒網(wǎng)模型是可行和有效的。3.針對(duì)金融系統(tǒng)因?yàn)檠蛉盒?yīng)而波動(dòng)的特點(diǎn),建立基于數(shù)據(jù)輔以機(jī)理分析的金融系統(tǒng)動(dòng)力學(xué)模型。研究了羊群效應(yīng)的機(jī)理和形成原因,分析總結(jié)了其通過數(shù)據(jù)對(duì)外表征的波動(dòng)形式,給出了間歇反饋的概念,通過正負(fù)方向帶起止閾值的死區(qū)函數(shù)疊加描述了間歇反饋的具體數(shù)學(xué)表達(dá)式。證明了用間歇反饋描述系統(tǒng)狀態(tài)控制量的可行性。結(jié)合多維泰勒網(wǎng)和間歇反饋,提出了間歇反饋多維泰勒網(wǎng)金融系統(tǒng)動(dòng)力學(xué)模型及其參數(shù)辨識(shí)方法。應(yīng)用實(shí)例通過對(duì)實(shí)際金融數(shù)據(jù)的建模驗(yàn)證了間歇反饋多維泰勒網(wǎng)模型的可行性,預(yù)測(cè)結(jié)果表明其優(yōu)于傳統(tǒng)非機(jī)理數(shù)據(jù)模型。4.針對(duì)間歇反饋多維泰勒網(wǎng)動(dòng)力學(xué)模型中,模擬羊群效應(yīng)的間歇反饋部分與多維泰勒網(wǎng)部分在進(jìn)行系統(tǒng)辨識(shí)時(shí)辨識(shí)針對(duì)性不精確的問題,建立基于參數(shù)交替迭代的優(yōu)化模型。為了平衡間歇反饋多維泰勒網(wǎng)動(dòng)力學(xué)模型中兩部分子模塊的所占比重,通過對(duì)多維泰勒網(wǎng)特性的挖掘,構(gòu)造了多重多維泰勒網(wǎng)(MMTN)的模型結(jié)構(gòu)。證明了多重多維泰勒網(wǎng)可以適用于相同狀態(tài)向量、不同目標(biāo)輸出的數(shù)據(jù)子集建模疊加�；诙嘀囟嗑S泰勒網(wǎng)的多重疊加性質(zhì),在間歇反饋多維泰勒網(wǎng)模型的基礎(chǔ)上,提出了基于帶間歇反饋的多重多維泰勒網(wǎng)金融系統(tǒng)動(dòng)力學(xué)模型建模方法。給出了其參數(shù)辨識(shí)的具體方法。實(shí)例結(jié)果表明其預(yù)測(cè)效果好于傳統(tǒng)非機(jī)理數(shù)據(jù)建模方法,同時(shí)也好于間歇反饋多維泰勒網(wǎng)動(dòng)力學(xué)模型。
[Abstract]:The financial system is the leading and hub of the rational allocation mechanism of market resources in the market economy. The normal operation of the financial system is the necessary condition to ensure the stability of the country's economic operation. The financial data includes the stock price, the deposit and loan, the fund, the insurance and the foreign exchange. It is the most important data type in the economic data. And prediction can provide guidance for the formulation of national macro-control. The establishment of a mathematical model of the financial system is the main approach to the study of the financial system. The existing model based on the operational mechanism of the financial system is mainly aimed at specific financial fields to solve specific problems, but the constraints are limited because of the complex and changeable structure of the golden thaw system. The non mechanism data modeling method, through the high speed operation of the computer, can quickly process a large amount of financial data and get more extensive application in the financial data analysis, but its existence is only concerned with the internal connection of the data and divorced from the actual problems. In order to establish a better financial model, it makes it for economic control and national macro-control research. In this paper, we propose a method for modeling and prediction of financial data based on multidimensional Taylor network (MTN), and further propose a method for modeling and forecasting the financial data of the multidimensional Taylor network (DCMTN), intermittent feedback multidimensional Taylor net (IFB-MTN) and multiple multidimensional Taylor network (MIMTN) with intermittent feedback based on its extended dynamic characteristics. Based on the data modeling of the financial system, the mathematical model is proposed and the corresponding model solving method is given. The main work of this paper is summarized as follows: 1. in view of the problems in the internal elements of the financial system and the complex structure of the financial system, the dynamic model of the financial system based on the data is established. In the form, combining the characteristics of the multi-dimensional state vector in the financial system and the basic principle of Taylor expansion, a dynamic model of multidimensional Taylor net is proposed. The rationality of the multidimensional Taylor net model expression is proved, the order of weighted terms and the recursive expression in the model are clarified. The iterative solution of the model parameters by the conjugate gradient method is obtained. In order to test the validity of the model, in order to test the validity of the model, the effect of the random disturbance in the financial data is reduced by the method of data filtering and decomposition. Then, the multidimensional Taylor net model is established for each subset of the decomposed data, and the parameters are identified and predicted. Finally, the prediction results are made. The simulation experiment results show the validity of the model and algorithm. It also lays the foundation for the extended study based on the multi-dimensional Taylor network model. The dynamic characteristics of the financial system in the financial system are fast, the structure and characteristics are changeable, and the dynamic prediction model of the dynamic characteristics of the financial system with different prediction targets is established. The dynamic characteristics of the fusion system, the dynamic characteristics are defined, and the rationality of the mathematical expression is proved. According to the similarity degree of the dynamic characteristics of the data points in the financial data, the specific form of the similarity of the dynamic characteristics is defined. The characteristics of the similarity are summarized and proved, and the multidimensional Taylor network and the dynamic characteristics are combined. And similarity, a dynamic prediction model of financial system based on dynamic characteristic clustering multi-dimensional Taylor net is proposed. The parameters of the model are identified by the least square estimation method. The results show that the dynamic clustering multi-dimensional Taylor net model is a feasible and effective.3. for the volatility of the financial system because of the herd effect. The dynamic model of financial system based on data and mechanism analysis is established. The mechanism and causes of the herd effect are studied. The fluctuation form of its external representation is analyzed and summarized. The concept of intermittent feedback is given. The specific mathematical expression of intermittent feedback is described by the superposition of dead zone function with the threshold threshold of positive and negative direction. The feasibility of describing the state control of the system with intermittent feedback is proved. Combined with multidimensional Taylor network and intermittent feedback, the dynamic model and parameter identification method of the intermittent feedback multidimensional Taylor network financial system are proposed. The feasibility of the intermission feedback multidimensional Taylor net model is verified by the actual financial data modeling. The test results show that it is superior to the traditional non mechanism data model.4. for the batch feedback multidimensional Taylor network dynamic model. The batch feedback part of the herd effect and the multidimensional Taylor net part identify the problem of inaccuracy in the system identification, and the optimization model based on the alternate iteration of parameters is established. In order to balance the intermittent feedback, the model is used to balance the intermittent feedback. The proportion of two molecular modules in the dynamic model of multidimensional Taylor network is constructed by mining the properties of multidimensional Taylor network. It is proved that the multi dimensional Taylor net (MMTN) model can be applied to the same state vector, the data subset of different target output is superimposed. The multi dimensional Taylor network based on multiple multidimensional Taylor network is used. On the basis of intermittent feedback multidimensional Taylor network model, the modeling method of dynamic model of multi dimensional Taylor net financial system based on intermittent feedback is proposed. The specific method of parameter identification is given. The results show that the prediction effect is better than the traditional non mechanism data modeling method, and it is also better than intermittent inverse. The dynamic model of feed multidimensional Taylor net.

【學(xué)位授予單位】：東南大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：F830;N945.14

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