本文選題：貝葉斯　切入點：LASSO　出處：《西南財經(jīng)大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：隨著中國經(jīng)濟和金融環(huán)境不斷地開放,經(jīng)濟金融方面的海量高維數(shù)據(jù)的不斷積累,大數(shù)據(jù)時代已經(jīng)到來。不僅大數(shù)據(jù)有其本身的價值,而且針對大數(shù)據(jù)進行建模分析的應(yīng)用價值也越來越明顯。一般來說,面對著同一數(shù)據(jù),研究人員可能會有許多可供選擇的模型,如何從較多模型中選擇出具有應(yīng)用價值的模型成為了理論界和實證界一直以來所共同關(guān)注的焦點。在1980年以前,統(tǒng)計學(xué)家對于模型選擇的研究方向較多地集中在信息準(zhǔn)則方面,比如AIC、BIC和Cp準(zhǔn)則,它們的原理簡單但計算的維度較高,當(dāng)變量較多的時候,如果要在所有的可能模型中選擇出滿足特定準(zhǔn)則最小的模型,這類方法面臨著實際的操作難度。因此,一個能夠大幅度地減少搜尋次數(shù)并且具有一定理論優(yōu)勢的研究方法開始被提出,其中Tibshirani(1996)所提出的Least Absolute Shrinkage and Selection Operation(簡稱LASSO)方法,不僅可以避免最小二乘法在高維條件下的不穩(wěn)定性,而且還能將不顯著的參數(shù)自動估計為零,達(dá)到模型選擇的目的,因此逐漸地成為了眾多研究者選擇模型的主要方法之一,其中,Efron(2004)提出的最小小角回歸(Iars)算法是目前比較流行的解決LASSO的快速而有效的方法之一。 由于LASSO方法在一定條件下等價于貝葉斯方法,因此,從貝葉斯的角度考慮模型選擇的研究也成為一種新的方向。而且,隨著貝葉斯方法在實踐中的應(yīng)用效果被許多研究者關(guān)注,由于LASSO方法可以用一種Laplace先驗分布的貝葉斯估計進行表示,因此,貝葉斯LASSO方法(Park,2008)逐漸地被正式地提出和被應(yīng)用。這種方法的主要特點在于,不僅它具有模型選擇的作用,而且還能發(fā)揮貝葉斯統(tǒng)計的優(yōu)點,運用MCMC方法進行參數(shù)的逼近估計在經(jīng)濟金融研究領(lǐng)域,研究者們普遍面對的數(shù)據(jù)是時間序列,針對時間序列的建模方法有許多,其中平穩(wěn)時間序列中三種基本方法即：AR模型、ARMA模型和ARCH模型。目前,從本論文所研讀的最新文獻來看,時間序列模型中采用LASSO方法的研究已有少許,但嘗試性地探討貝葉斯LASSO方法在平穩(wěn)時間序列模型中應(yīng)用效果的研究幾乎沒有。基于這樣的理論和現(xiàn)實背景,本文嘗試將貝葉斯LASSO方法應(yīng)用于平穩(wěn)時間序列模型中。 本文主要從理論和實證兩個方面研究了貝葉斯LASSO在平穩(wěn)時間序列模型中的應(yīng)用效果。理論方面,首先,本文從平穩(wěn)時間序列基本方法、LASSO的發(fā)展和應(yīng)用現(xiàn)狀、貝葉斯LASSO的發(fā)展和應(yīng)用現(xiàn)狀等三個方面綜述了已有的研究成果,并討論了貝葉斯LASSO方法在平穩(wěn)時間序列模型中的推廣的可能性及意義所在,形成本文的理論基礎(chǔ)。其次,本文從LASSO的基本思想、貝葉斯基本原理和貝葉斯LASSO方法三個方面,逐層次地將LASSO和貝葉斯緊密地聯(lián)系在一起。再次,本文分別詳細(xì)介紹了三種基本平穩(wěn)時間序列模型：AR模型、ARMA模型和ARCH模型,并通過數(shù)據(jù)變換的處理方式,成功地從理論上說明貝葉斯LASSO方法應(yīng)用到上述三種模型中的可行性。最后,通過R軟件平臺,本文應(yīng)用現(xiàn)有的貝葉斯LASSO算法,分別將貝葉斯LASSO方法應(yīng)用在AR模型、ARMA模型和ARCH模型的數(shù)據(jù)模擬分析之中,驗證了三種模型的模擬應(yīng)用的效果。實證方面,本文主要輸入了上證300指數(shù)的數(shù)據(jù),對指數(shù)的日對數(shù)收益率數(shù)據(jù)進行了波動率的ARCM建模分析,并將實證結(jié)果與一般的ARCM模型進行了對比,結(jié)果表明本文的方法在ARCM波動率實證研究中的嘗試具有一定的可行性效果。 本文的主要結(jié)論包括： (一)平穩(wěn)時間序列模型的估計可以運用貝葉斯LASSO方法進行解決,并能夠取得一定的效果,但并非總是優(yōu)于LASSO。因為,本論文的數(shù)據(jù)模擬分析發(fā)現(xiàn),在適當(dāng)?shù)臉颖救萘織l件下,本文方法的正確率在有的條件下對某些參數(shù)而言是高于LASSO方法的,有的條件下也是低于LASSO的。 (二)貝葉斯LASSO方法能夠提供更多的概率決策信息。因為,本文所采用的方法屬于貝葉斯框架的分析方法,故可以提供更可靠的區(qū)間估計等信息。本論文的算法是通過MCMC模擬確定了樣本后驗分布的穩(wěn)定性,我們從該分布中分析出很多的信息,如本文所定義的“變量接受概率”,它可以根據(jù)實際情況根據(jù)樣本量和時間序列維數(shù)進行合理的設(shè)置,當(dāng)樣本量比較大的時候,設(shè)置較高的接受概率可以準(zhǔn)確選擇出合理的變量,當(dāng)樣本量逐漸下降的時候,某些參數(shù)的變量接受概率會隨著樣本量的下降而不斷降低。
[Abstract]:With the China economic and financial environment constantly open, the accumulation of massive high-dimensional data of economic and financial aspects of the era of big data has arrived. Not only big data has its own value, but also the application value of the modeling and analysis for big data is becoming more and more obvious. In general, faced with the same data, researchers may there will be many alternative models, how to choose from the many models of the model value has become the focus of theoretical and empirical circles has been a common concern. Before 1980, statisticians for more research direction of model selection on information standards, such as AIC, BIC and Cp criterion. The principle is simple but the computation of high dimension, when there are more variables, if possible in all models selected to meet specific criteria of minimum model, facing this kind of method The difficulty of the operation. Therefore, one can greatly reduce the search times and the research method has certain theoretical advantages was proposed, in which Tibshirani (1996) proposed by Least Absolute Shrinkage and Selection Operation (LASSO) method can not only avoid the least squares method in high dimension under the condition of instability zero automatic parameter estimation but also will not be significant, achieve the purpose of model selection, thus gradually become one of the main methods, many researchers choose to model the Efron (2004) proposed the minimum small angle regression (Iars) algorithm is a popular solution for LASSO rapid and effective method of.
Because the LASSO method under certain conditions is equivalent to the Bayesian method, therefore, from the point of view of Bayesian model selection has become a new direction. Moreover, with the application of Bayesian method in practice by many researchers, because LASSO method can estimate that with a prior distribution in Bayesian Laplace therefore, Bayesian LASSO method (Park, 2008) has been formally put forward and is applied. The main characteristic of this method is that it not only has the model choice for the role, but also play the advantages of Bayesian statistics, using MCMC method of parameter estimation approach in the economic field of financial research, researchers generally face data is the time series, according to the modeling method of time series are many, including three kinds of basic methods of stationary time series: AR model, ARMA model and ARCH model. First, from the latest literature in this thesis study, LASSO method is used in time series model has a little research, but the study attempts to explore Bias LASSO method application in stationary time series model hardly. Based on this theoretical and practical background, this paper tries to Bias LASSO method is applied to stationary time the sequence of the model.
This paper mainly from two aspects of theory and empirical research on the application of Bias LASSO in the stationary time series model. The theory, first, from the basic method of stationary time series, the development and application status of LASSO, the three aspects of Bias LASSO's development and application of the existing research results, are discussed. Bias LASSO method in stationary time series model in the promotion of the possibility and significance of the formation of the theoretical basis of this paper. Secondly, this article from the basic idea of LASSO, the three aspects of the basic principle of Bias and Bias LASSO method, by level LASSO and Bias closely together. Thirdly, this paper introduces in detail three basic stationary time series models: AR model, ARMA model and ARCH model, and through the processing method of data transformation, successfully explains Bias LASSO theoretically. The method applied to the feasibility of the three models. Finally, through the R software platform, this paper uses Bias existing LASSO algorithm, respectively, the application of Bias method in the LASSO AR model, ARMA model and ARCH model of data simulation, to verify the three models to simulate the application effect. The empirical aspect, this paper enter the Shanghai 300 index data was analyzed by ARCM modeling the volatility of daily logarithmic return rate index data, and empirical results and the general ARCM model were compared. The results show that this method has certain effect to rate the feasibility in empirical research on the ARCM wave.
The main conclusions of this paper include:
(a) estimation of stationary time series model can be used to solve the Bayesian LASSO method, which can obtain a certain effect, but is not always better than that of LASSO. because the data analysis found that in the condition of sample size is proper, the correct rate of this method is higher than that of LASSO method for some parameters in some conditions under some conditions is less than LASSO.
(two) Bias LASSO method can provide more information for probabilistic decision analysis method, this method belongs to the Bias framework, it can provide more reliable information of interval estimation. The algorithm is proved the stability of distribution determines the sample through MCMC simulation, we analyze a lot of information from the the distribution, as defined herein "variable acceptance probability", it can according to the actual situation according to the sample size and the dimension of time series reasonable setting, when the sample size is relatively large, a higher probability of acceptance can accurately select the reasonable variables, when the sample size decreases gradually, some parameters variable acceptance probability will continue to decrease with the decrease of sample size.

【學(xué)位授予單位】：西南財經(jīng)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：O211.61;F830.91

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