本文關(guān)鍵詞： 長記憶性 長記憶誤差項(xiàng) 近似因子模型 VARFIMA模型　出處：《浙江財(cái)經(jīng)大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：金融時(shí)間序列的研究是時(shí)間序列研究的一個(gè)重要分枝。金融時(shí)間序列既有在時(shí)間序列大框架下的共性,同時(shí)又有區(qū)別于其他序列的特性,比如數(shù)據(jù)的分布往往呈現(xiàn)出尖峰厚尾的特點(diǎn),數(shù)據(jù)波動(dòng)的異方差性以及波動(dòng)集聚性,自相關(guān)性,長記憶特征等等。研究者對(duì)于長記憶性的認(rèn)識(shí)起源于自然科學(xué),深耕于經(jīng)濟(jì)、金融等領(lǐng)域。本文主要所研究的對(duì)象是包含長記憶特征的多維時(shí)間序列。本文的目的在于對(duì)多維長記憶時(shí)間序列進(jìn)行近似因子模型分析,確定因子個(gè)數(shù)。對(duì)于此,本文在近似因子模型的框架下,針對(duì)存在長記憶性的多維時(shí)間序列,提出存在長記憶誤差項(xiàng)的近似因子模型,并提出了確定該模型中因子個(gè)數(shù)的估計(jì)方法,通過理論和模擬呈現(xiàn)了該方法具有估計(jì)一致性的特點(diǎn)。模擬中表明,在不同的長記憶參數(shù)下,該估計(jì)方法表現(xiàn)出穩(wěn)健性。在實(shí)證中,本文首先研究了全球股票市場(chǎng)之間的聯(lián)動(dòng)關(guān)系。其次研究了中國股票市場(chǎng)中二十個(gè)行業(yè)板塊指數(shù),運(yùn)用本文所提出的模型來確定這些行業(yè)板塊指數(shù)因子的個(gè)數(shù)。本文的主要?jiǎng)?chuàng)新和貢獻(xiàn)集中在建立了存在長記憶誤差項(xiàng)的近似因子模型,這是對(duì)當(dāng)前近似因子模型的一個(gè)拓展,因?yàn)橐延械慕埔蜃幽Ｐ?考慮的是誤差項(xiàng)的序列相關(guān)和截面相關(guān)的情況,還未在因子模型中考慮誤差項(xiàng)的長期相依性。同時(shí),本文提出了該模型中因子個(gè)數(shù)的估計(jì)方法。這一估計(jì)方法主要分為兩步,首先,將原時(shí)間序列進(jìn)行長記憶性分解,得到長記憶部分和非長記憶部分。隨后用近似因子模型的方法對(duì)非長記憶部分進(jìn)行因子個(gè)數(shù)的選取,在這一步中,基于BIC和IC準(zhǔn)則,提出了估計(jì)因子個(gè)數(shù)新的準(zhǔn)則。理論結(jié)果證明該估計(jì)方法可以一致地估計(jì)出真實(shí)的因子個(gè)數(shù)。在統(tǒng)計(jì)模擬中,將本文提出的方法同直接使用IC、AIC和BIC準(zhǔn)則選取因子的方法做比較。模擬結(jié)果發(fā)現(xiàn),當(dāng)長記憶參數(shù)值較大時(shí),本文提出的方法可以準(zhǔn)確地估計(jì)出真實(shí)的因子的個(gè)數(shù),并且要遠(yuǎn)遠(yuǎn)好于其他方法。當(dāng)長記憶參數(shù)值較小時(shí),本文提出的方法略微遜色使用IC方法,但是仍然可以較為準(zhǔn)確地估計(jì)出因子個(gè)數(shù)�？傮w來說,本文提出的方法對(duì)于不同的長記憶性參數(shù),估計(jì)值表現(xiàn)出良好的穩(wěn)健性,平均表現(xiàn)優(yōu)于通過AIC,BIC和IC準(zhǔn)則來確定因子個(gè)數(shù)。
[Abstract]:The study of financial time series is an important branch of time series research. For example, the distribution of data often shows the characteristics of peak and thick tail, heteroscedasticity and agglomeration of data fluctuations, autocorrelation, long memory characteristics and so on. The purpose of this paper is to analyze the multidimensional long memory time series with approximate factor model and determine the number of factors. In this paper, an approximate factor model with long memory error term is proposed for multidimensional time series with long memory, and a method to estimate the number of factors in the model is proposed. The theory and simulation show that the method is consistent in estimation. The simulation shows that the method is robust under different long memory parameters. This paper first studies the linkage between global stock markets, and then studies 20 industry sector indices in Chinese stock markets. The main innovation and contribution of this paper is to establish an approximate factor model with long memory error term, which is an extension of the current approximate factor model. Because of the existing approximate factor model, the sequence correlation and cross-section correlation of the error term are considered, and the long-term dependence of the error term has not been considered in the factor model. In this paper, a method for estimating the number of factors in the model is proposed. The method is divided into two steps. Firstly, the original time series are decomposed into long memory. The long memory part and the non long memory part are obtained. Then the approximate factor model is used to select the number of factors for the non long memory part. In this step, based on the BIC and IC criteria, A new criterion for estimating the number of factors is proposed. The theoretical results show that the method can estimate the number of real factors consistently. The method proposed in this paper is compared with the method of selecting factors by using ICG AIC and BIC criterion directly. The simulation results show that when the value of long memory parameter is large, the method presented in this paper can accurately estimate the number of real factors. And it is much better than other methods. When the value of long memory parameter is small, the method proposed in this paper is slightly inferior to the IC method, but it can still estimate the number of factors more accurately. The method presented in this paper shows good robustness for different long memory parameters, and the average performance is better than that of determining the number of factors by AICBIC and IC criteria.
【學(xué)位授予單位】：浙江財(cái)經(jīng)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：F224;F831.51

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本文編號(hào)：1502010