本文選題：單位根檢驗(yàn) + 經(jīng)驗(yàn)似然比統(tǒng)計(jì)量�。� 參考：《浙江工商大學(xué)》2017年碩士論文

【摘要】：單位根檢驗(yàn)是計(jì)量經(jīng)濟(jì)學(xué)中十分重要的研究?jī)?nèi)容之一。尤其在實(shí)際的金融時(shí)間序列多為非線性,并且大多數(shù)是含有單位根的非平穩(wěn)序列的背景下,平穩(wěn)性檢驗(yàn)在研究時(shí)間序列數(shù)據(jù)中已是必不可少的一個(gè)步驟。但是傳統(tǒng)的單位根檢驗(yàn)是基于線性模型提出的,針對(duì)現(xiàn)今眾多非線性模型的檢驗(yàn)效果并不是十分有效,容易造成過分接受非平穩(wěn)的假設(shè),從而引起誤判�；诖�,本文針對(duì)實(shí)際應(yīng)用較多的非線性STAR模型進(jìn)行了相應(yīng)的單位根檢驗(yàn)研究。考慮到STAR模型在實(shí)際擬合時(shí)間序列數(shù)據(jù)時(shí),模型的殘差項(xiàng)常服從GARCH過程,因此本文在前人的基礎(chǔ)上構(gòu)建了檢驗(yàn)似然比檢驗(yàn)統(tǒng)計(jì)量l(δ)。似然比檢驗(yàn)統(tǒng)計(jì)量極大的提高了 STAR模型的單位根檢驗(yàn)功效,并且與汪盧俊(2014)提出的針對(duì)LSTAR-GARCH模型的單位根檢驗(yàn)統(tǒng)計(jì)量tNG相比,避免了計(jì)算估計(jì)方差,有效的降低了計(jì)算復(fù)雜度,提高了估計(jì)統(tǒng)計(jì)量的穩(wěn)定性。本文首先是對(duì)單位根檢驗(yàn)的歷史和理論進(jìn)行了介紹,然后基于汪盧俊(2014)提出的針對(duì)LSTAR-GARCH模型的單位根檢驗(yàn)統(tǒng)計(jì)量tNG,在文中第三章創(chuàng)造性的提出了基于LSTAR-GARCH模型的經(jīng)驗(yàn)似然比檢驗(yàn)統(tǒng)計(jì)量l(δ),并推導(dǎo)出其極限分布。其中關(guān)于時(shí)間序列的條件方差時(shí)變性特征(GARCH項(xiàng)),tNG的極限分布在推導(dǎo)過程中需要考慮到tNG的估計(jì)方差,這樣會(huì)增加tNG的不穩(wěn)定性和計(jì)算復(fù)雜度,而經(jīng)驗(yàn)似然比檢驗(yàn)統(tǒng)計(jì)量可以有效地避免計(jì)算統(tǒng)計(jì)量的估計(jì)方差,從而提高單位根檢驗(yàn)的效果。為了驗(yàn)證第三章中的理論,本文第四章通過蒙特卡羅和Bootstrap方法進(jìn)行模擬和功效比較,在模擬的角度進(jìn)一步的說明這一情況。更進(jìn)一步,第五章結(jié)合我國上證指數(shù)股票數(shù)據(jù)進(jìn)行實(shí)證分析,通過擬合情況來比較,說明使用經(jīng)驗(yàn)似然比檢驗(yàn)統(tǒng)計(jì)量檢驗(yàn),構(gòu)建的STAR模型最為準(zhǔn)確,能夠?yàn)橥顿Y者提供更可靠的信息。
[Abstract]:Unit root test is one of the most important research contents in econometrics. Especially under the background that the actual financial time series are mostly nonlinear and most of them are non-stationary sequences with unit roots, the stationary test is an essential step in the study of time series data. However, the traditional unit root test is based on the linear model. The test effect for many nonlinear models is not very effective. It is easy to overaccept the assumption of non-stationary, thus causing misjudgment. Based on this, this paper studies the unit root test of nonlinear STAR model which is widely used in practice. Considering that the residual term of the STAR model is usually followed by the GARCH process when the time series data are fitted, the test likelihood ratio test statistic L (未) is constructed on the basis of previous studies. Likelihood ratio test statistics greatly improve the efficiency of unit root test of STAR model, and compared with the unit root test statistic tNG for LSTAR-GARCH model proposed by Wang Lujun 2014, it avoids the estimated variance and reduces the computational complexity effectively. The stability of estimation statistics is improved. This paper first introduces the history and theory of unit root test. Then, based on the unit root test statistic for LSTAR-GARCH model proposed by Wang Lujun (2014), the empirical likelihood ratio test statistic based on LSTAR-GARCH model is creatively proposed in chapter 3, and its limit distribution is deduced. For the conditional variance of time series, it is necessary to take into account the estimated variance of tNG in the derivation of the limit distribution of the term GARCH, which will increase the instability and computational complexity of tNG. The empirical likelihood ratio test statistics can effectively avoid calculating the estimated variance of the statistics and thus improve the effect of unit root test. In order to verify the theory in the third chapter, the fourth chapter of this paper uses Monte Carlo and Bootstrap methods to simulate and compare the effectiveness of the simulation, in order to further explain this situation in the perspective of simulation. Furthermore, the fifth chapter combines the stock data of Shanghai Stock Exchange of China to carry on the empirical analysis, through the comparison of the fitting situation, shows that using the empirical likelihood ratio test statistic test, the STAR model is the most accurate. To provide investors with more reliable information.
【學(xué)位授予單位】：浙江工商大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：F224;F832.51

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本文編號(hào)：1836535