本文選題：長記憶序列　切入點(diǎn)：結(jié)構(gòu)變點(diǎn)　出處：《西安科技大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：自20世紀(jì)80年代以來,長記憶時(shí)間序列理論開始在計(jì)量經(jīng)濟(jì)學(xué)領(lǐng)域中得到快速發(fā)展,并廣泛應(yīng)用在經(jīng)濟(jì)、金融等研究領(lǐng)域;與此同時(shí),變點(diǎn)檢測問題也同樣受到經(jīng)濟(jì)學(xué)家的高度重視。時(shí)下,越來越多的金融數(shù)據(jù)呈現(xiàn)長記憶特性,而且結(jié)構(gòu)變點(diǎn)在金融時(shí)間序列中經(jīng)常出現(xiàn)。鑒于此,研究長記憶序列指數(shù)變點(diǎn)檢驗(yàn)問題顯得十分重要。本文的創(chuàng)新點(diǎn)如下:首先,建立含指數(shù)變點(diǎn)的長記憶序列回歸模型,基于ratio檢驗(yàn)統(tǒng)計(jì)量檢驗(yàn)序列的指數(shù)變點(diǎn)。研究發(fā)現(xiàn):在原假設(shè)下,ratio檢驗(yàn)統(tǒng)計(jì)量收斂到一個(gè)分?jǐn)?shù)布朗橋,在備擇假設(shè)下,ratio檢驗(yàn)統(tǒng)計(jì)量是發(fā)散的。數(shù)據(jù)模擬結(jié)果表明:在原假設(shè)下,拒絕率隨樣本量的增大而增大,基本接近5%,在備擇假設(shè)下,拒絕率隨樣本量的增大以及指數(shù)跳躍幅度的增大而增大,最高達(dá)到66.3%。此外,變點(diǎn)的估計(jì)依賴于不同的長記憶時(shí)間序列和樣本量,更加準(zhǔn)確地說,隨著指數(shù)跳躍幅度的增大,變點(diǎn)的估計(jì)值會(huì)更加精確,接近真實(shí)值。通過蒙特卡羅模擬說明理論與實(shí)驗(yàn)?zāi)M相吻合。其次,建立含均值變點(diǎn)、指數(shù)變點(diǎn)的長記憶序列回歸模型,基于ratio檢驗(yàn)統(tǒng)計(jì)量檢測序列的指數(shù)變點(diǎn)。研究發(fā)現(xiàn):在原假設(shè)下,ratio檢驗(yàn)統(tǒng)計(jì)量是以021 dT-的速率發(fā)散,在備擇假設(shè)下,ratio檢驗(yàn)統(tǒng)計(jì)量趨于無窮。數(shù)據(jù)模擬結(jié)果表明:在原假設(shè)下,拒絕率隨著均值跳躍幅度的增大而增大,隨著長記憶指數(shù)的增大而減小,且均值起決定性作用,這有可能導(dǎo)致過高地估計(jì)指數(shù),甚至導(dǎo)致研究者產(chǎn)生誤判,在備擇假設(shè)下,拒絕率隨著均值跳躍幅度增大以及指數(shù)跳躍幅度的增大而增大,并趨于無窮,均值的影響相對較大。通過蒙特卡羅模擬驗(yàn)證理論的合理性與正當(dāng)性。綜上所述,對以上兩種長記憶回歸模型,均能利用ratio檢驗(yàn)統(tǒng)計(jì)量有效檢驗(yàn)長記憶指數(shù)變點(diǎn),同樣地,數(shù)值模擬也能驗(yàn)證理論的合理性與正當(dāng)性。
[Abstract]:Since 1980s, the theory of long memory time series has been developing rapidly in the field of econometrics, and has been widely used in the fields of economics, finance and so on. Nowadays, more and more financial data show long memory characteristics, and structural change points often appear in financial time series. It is very important to study the problem of exponential change point test of long memory sequence. The innovation of this paper is as follows: firstly, the regression model of long memory sequence with exponential change point is established. Based on the exponential change point of the ratio test statistic test sequence, it is found that the ratio test statistic converges to a fractional Brownian bridge under the original hypothesis, and the ratio test statistic is divergent under the alternative hypothesis. The data simulation results show that: under the original hypothesis, the ratio test statistic is divergent. The rejection rate increases with the increase of the sample size and is close to 5. Under the alternative assumption, the rejection rate increases with the increase of the sample size and the jump amplitude of the index, and the highest value is 66.3%. The estimation of the change point depends on different long memory time series and sample size. More accurately, with the increase of the jump amplitude of the index, the estimation of the change point will be more accurate. Close to the real value. Monte Carlo simulation shows that the theory is consistent with the experimental simulation. Secondly, a long memory sequence regression model with mean and exponential change points is established. Based on the exponential change point of the ratio test statistics, it is found that the ratio test statistics diverge at the rate of 0.21 dT- under the original hypothesis, and the statistics of the ratio test tend to infinity under the alternative hypothesis. The data simulation results show that: under the original hypothesis, the ratio test statistics tend to be infinite. The rejection rate increases with the increase of the mean jump amplitude and decreases with the increase of the long memory index, and the mean value plays a decisive role, which may lead to overestimation of the index, and even lead to the misjudgment of the researcher. The rejection rate increases with the increase of the mean jump amplitude and the exponential jump amplitude, and tends to infinity. The influence of the mean value is relatively large. The validity and rationality of the theory are verified by Monte Carlo simulation. For the above two kinds of long memory regression models, the ratio test statistics can be used to test the long memory index variation points effectively. Similarly, numerical simulation can also verify the rationality and legitimacy of the theory.
【學(xué)位授予單位】：西安科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212

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