本文關(guān)鍵詞：協(xié)變量驅(qū)動(dòng)的隨機(jī)系數(shù)自回歸模型參數(shù)估計(jì)　出處：《吉林大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 隨機(jī)系數(shù) 自回歸模型 條件最小二乘估計(jì) 極大似然估計(jì) 貝葉斯估計(jì)

【摘要】：時(shí)間序列分析一直是統(tǒng)計(jì)學(xué)的一個(gè)重要分支,主要分為線性時(shí)間序列模型與非線性時(shí)間序列模型.關(guān)于線性時(shí)間序列模型的研究結(jié)果目前已經(jīng)比較成熟,但由于實(shí)際生活中的部分?jǐn)?shù)據(jù)不符合線性時(shí)間序列模型.因此,在近幾十年來,非線性時(shí)間序列模型越來越受到國內(nèi)外學(xué)者的關(guān)注,并取得了不錯(cuò)的研究成果.其中,隨機(jī)系數(shù)自回歸模型是非線性時(shí)間序列的一種,它與Logistic回歸模型在實(shí)際生活中都有著廣泛的應(yīng)用,但目前國內(nèi)外學(xué)者將兩者結(jié)合起來的研究還非常稀少.基于此,本文提出了一個(gè)全新的隨機(jī)系數(shù)自回歸模型:其中隨機(jī)誤差序列{(?)t}i.i.d服從Laplace(0,1)分布,自回歸系數(shù)αt是隨機(jī)變量,服從包含協(xié)變量Z的Logistic回歸模型,這也是本文的創(chuàng)新之處.本文的主要工作是運(yùn)用基于條件期望的最小二乘估計(jì)、極大似然估計(jì)及貝葉斯估計(jì)方法對(duì)一階Logistic回歸模型的參數(shù)β1,β2進(jìn)行估計(jì).但是,Logistic回歸模型中涉及到了對(duì)數(shù)函數(shù),函數(shù)表達(dá)式較為復(fù)雜,因此在做參數(shù)估計(jì)時(shí)考慮使用Taylor展開近似,將復(fù)雜的表達(dá)式化為多項(xiàng)式的形式,得出近似估計(jì)表達(dá)式.而對(duì)不能解出顯式參數(shù)估計(jì)表達(dá)式的方程運(yùn)用Matlab利用數(shù)值分析方法給出數(shù)值解.最后對(duì)所提出的方法進(jìn)行數(shù)值模擬和實(shí)證分析,比較不同方法的優(yōu)劣并給出結(jié)論.
[Abstract]:Time series analysis has been an important branch of statistics, mainly divided into linear time series model and nonlinear time series model. However, some of the data in real life do not accord with the linear time series model. Therefore, in recent decades, the nonlinear time series model has attracted more and more attention from domestic and foreign scholars. The random coefficient autoregressive model is a kind of nonlinear time series, which is widely used in real life with Logistic regression model. However, there are few researches on the combination of the two at home and abroad. Based on this, a new autoregressive model with random coefficients is proposed in this paper: where the random error sequence {? The autoregressive coefficient 偽 t was a random variable, and the Logistic regression model containing covariable Z was used. This is also the innovation of this paper. The main work of this paper is to use the least square estimation based on conditional expectation, maximum likelihood estimation and Bayesian estimation to the parameter 尾 1 of the first-order Logistic regression model. But the logarithmic function is involved in the logistic regression model, and the expression of the function is more complicated. Therefore, the Taylor expansion approximation is considered in the parameter estimation. Transform complex expressions into polynomial forms. The approximate estimation expression is obtained. Matlab is used to give the numerical solution for the equation which can not solve the explicit parameter estimation expression. Finally, the numerical simulation and empirical analysis of the proposed method are carried out. . The advantages and disadvantages of different methods are compared and the conclusions are given.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O212.1

【參考文獻(xiàn)】

相關(guān)博士學(xué)位論文 前1條

1 趙志文;自回歸模型的估計(jì)與檢驗(yàn)[D];吉林大學(xué);2011年

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本文編號(hào)：1396797