臺灣博碩士論文加值系統

在時間序列模型中，我們所碰到的幾乎都是非獨立的資料。在不知道母體的分布是什麼的情況下， Owen(1988)所提出的經驗概似法(Empirical Likelihood Estimation)已被廣泛應用在統計獨立的資料，這個方法已被證明優於其他已知的動差方法(Method of Moments)。後來，有一些統計學家試著把經驗概似法應用在非獨立的資料上; 在Kitamura(1997)之後，有許多文章的主題是關於如何把經驗概似法應用在弱相關(weakly dependent)或強相關(strongly dependent)資料上。在這篇論文中，我們將用經驗概似法去估計計量經濟模型的參數，這些模型包括ARCH，GARCH，EGARCH和TGARCH。我們比較了最大概似法或最小平方法與經驗概似法的模擬結果，最後我們利用GARCH模型來配適西德州原油資料，我們發現其結果與假設常態擾動之下最大概似法一致。

In most time series models, the data sets that we might
be confront with are not statistically independent. While the celebrated empirical likelihood (EL) estimation proposed by owen (1988) has been widely used in a framework of independent data without having to know the distribution of the population, it is also challenging to apply EL estimation to the models with dependent data. After Kitamura (1997), there has been a lot of papers focus on
the topic of how to apply EL method to a data set with dependence (short-range dependence or long-range dependence ). In this thesis,we will exploit EL method to estimate the parameters emerging in some important econometrical models including ARCH, GARCH, EGARCH
and TGARCH. In addition, we conduct some illustrative simulations to compare EL approach with other methods of estimation (e.g. MLE and OLS). Finally, we analyze the data of the West Texas Intermediate (WTI) Crude Oil Prices by fitting it into the GARCH model.

1 Introduction 1
2 Survey of Time Series Models and Related Estimations 6
2.1 AR(p) models.................................6
2.2 ARMA Models..................................8
3 Empirical Likelihood Estimation and its Application to EconometricalModels 10
3.1 The ARCH Models.............................10
3.2 The Generalized ARCH Models (GARCH).........17
3.3 The Exponential GARCH Models (EGARCH).......23
3.4 The Threshold GARCH Models (TGARCH).........25
4 Simulation Study And Data Analysis 26
References 35

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