臺灣博碩士論文加值系統

本文針對時間序列線性迴歸，在我們假設的模型下估計出β參數值。透過兩種不同的估計方法進行分析，第一種是最小平方法，第二種是新方法，新方法是利用迴旋積分推導出Y的機率密度函數和Likelihood Function，在獲得參數估計的過程中由於積分計算量太大所以我們利用了Monte Carlo Methods逼近，在本文第三章有詳細介紹新方法估計式的推導。但是在新方法的估計式中Monte Carlo Method所計算出來的Likelihood值在因變數Y及自變數X差異過大時其值會太小，所以我們進行資料上的篩選讓Likelihood值在現有給予的資料上盡可能靠近最佳值，進而使Newton Raphson Method估計出不錯的β參數值。最後，我們模擬資料應用於這兩種方法，比較他們的估計結果。

The time series regression provides an explicit analysis, in which one time series (dependent variable) can be expressed linearly related to other time series variables (covariates), and often errors of the model are possibly correlated or simply white noises. The method of least squares is a naive approach to estimate the regression conditioned on the covariates. When the covariates are non-Gaussian stochastic time series, the least square estimators may not be quite efficient. We propose a new method taking into account the distribution properties. We estimate the parameters by maximizing the unconditional likelihood, which is obtained via convolution. The calculation of multi-fold convolution is insurmountable, so we approximate the unconditional likelihood using Monte Carlo, in which covariates are re-sampled and only selected probability weights are counted into the approximation. The maximum likelihood estimation is obtained applying the Newton-Raphson iterations on the approximated likelihood function. Simulation examples are given and the results are compared to the least squares estimates.

目錄
摘　要 I
謝　誌 III
目錄 IV
第壹章　緒　論 1
第一節　研究背景與動機 1
第二節　研究目的 3
第三節　研究流程 4
第貳章　文獻回顧 5
第一節　EIAR、EAR 5
1.1　EIAR 5
1.2　EAR 7
第二節　BGAR 9
第參章　研究方法 10
第一節　模型假設 10
第二節　估計式推導 11
第肆章　數據取樣 15
第一節　原始資料生成 15
第二節　重新抽取資料 16
第三節　資料篩選 17
第伍章　邊際值的選取 21
第陸章　分析結果 24
第柒章　結論 26
參考文獻 27

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