本研究有助於異質變異迴歸模型的係數估計。我們提出一套估計方法，透過牛頓法及合適的起始值達到估計係數的目的，並得到此估計係數的標準差。我們接著將此套方法應用到高維質變異迴歸模型選取，利用我們提出的微調參數之選取方法，由資料自行推薦最終模型。我們亦透過模擬與實證分析，來驗證我們提出方法的效果。

This study aims at estimating the coefficients in regression models with time series and heteroscedastic errors. A Newton-Raphson method is used in conjunction with suitable initial values to achieve this goal. Moreover, the standard deviations of the coefficient estimates
are found throughout heuristic derivations and some calculations. We then apply to the high-dimensional heteroscedastic model selection, and use our proposed data-driven approach to the selection of tuning parameters. Some simulation studies and a real data analysis are performed to illustrate the effectiveness of the proposed approaches.

摘要ii
1 Introduction 1
2 Main Result 4
2.1 Liklihood Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Asymptotic Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3 Simulation 11
3.1 Initial Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 Coefficients Estimation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4 Application 18
4.1 Model Selection Procedure: Twohit . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.2 Selection of Tuning Parameters in Twohit . . . . . . . . . . . . . . . . . . . . . 21
4.3 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5 Real Data Analysis 24
6 Conclusion 27

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