臺灣博碩士論文加值系統

本研究考慮具有外生變數和偏態Student-t誤差分配的分段自我迴歸不對稱GARCH模型。此模型稱為分段結構改變自我迴歸不對稱GARCH模型。本研究延伸到偏態Student-t分配在此模式架構，與其他分配相比，厚尾偏態Student-t分配在描述金融市場中的金融時間序列數據集方面表現極佳。本研究採用數個不同誤差分配的多個結構性改變的分段GARCH族群模型;除了模型中的未知參數，改變點的數目和位置也是未知的，我們採用貝氏方法的估計所有未知參數。通過貝氏推理估計模型參數，以顯示貝氏方法的有效性和可靠性。我們使用adaptive MCMC演算法，加速MCMC收斂。為識別斷點的數目及其位置，假設斷點的數目是預先固定的，並使用貝氏偏差信息量準則(DIC)來確定斷點的最佳數目以及最佳模型。本研究在模擬過程中探討模型選擇的準確率，並用模擬和實證分析結果來闡明所提的貝氏方法的可信度。對於實證分析，我們研究了2007年至2019年期間每日黃金報酬率和VIX對S&P 500指數報酬率的影響，結果顯示具有兩個斷點的不對稱GARCH模型是最佳的模型。

This research considers a piecewise autoregressive GARCH-type model with exogenous variables and skew Student-t errors, which we call a segmented ARX-GARCH model, and uses it to identify the location of structural breaks and to make inferences about all unknown parameters. Our model fills the gap in the existing literature by considering skew Student-t errors and proving the advantages of the fat-tailed skew Student-t distribution versus other distributions when studying financial time-series datasets. It is also able to detect the number of structural change points and their location in time series data by assuming the number of breakpoints is prefixed and employing deviance information criterion (DIC) to decide the optimal number of breakpoints. We also extend the segmented GARCH model to an asymmetric GARCH model and make inference about the parameters by employing the Bayesian approach, which is more efficient and reliable than conventional approaches. We utilize the adaptive Metropolis-Hastings Markov Chain Monte Carlo (MH-MCMC) methods by starting with the random walk MH algorithm and then moving to the independent kernel MH algorithm after the burn-in period for GARCH parameters in order to accelerate convergence. A simulation study’s results illustrate the credibility of our MCMC sampling scheme. For real data analysis, we examine the impact of daily gold returns and VIX on S&P 500 returns during 2007 to 2019. The empirical results show that our model is able to efficiently detect multiple structural changes and to capture the time-varying parameters in different segments. The proposed model can serve as an important element for strategy implementation, but also for the assessment of financial markets.

1 Introduction
2 The Structure Change Model
2.1 ARX-GARCH Model
2.2 ARX-GJR-GARCH Model
3 Bayesian methods
4 Simulation study
5 Empirical example
6 Conclusions and future research

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