本論文提出了一種全新的模型架構——基於階層向量Copula 之一階馬可夫過程，旨在捕捉多維度時間序列資料中複雜的相依結構。傳統的Copula 模型在應用於標準多元分配時，經常面臨運算瓶頸或過於嚴苛的理論假設。為突破這些限制，本研究提出一套具備高度普適性的方法論，能有效將橫斷面（空間）的相關性與時間軸上的相依性進行剝離。透過數學轉換技術，將具相依性的變數映射為獨立元件，本模型得以在不仰賴傳統侷限性設定的情況下，推導出精確且具備可運算性的聯合機率密度函數。在模型參數估計方面，本研究採用穩健 的混合估計策略，結合最大概似估計法(MLE) 與邊際推論法(IFM)，以確保運算上的穩定性與漸近效率。本研究亦透過全面的模擬研究與全球金融海嘯之實證分析，驗證了此模型架構的數學嚴謹性與實務應用價值。整體而言，研究結果證實此一新架構為刻畫多維度資料中不對稱的風險蔓延與極端尾部波動，提供了一個穩健、靈活且極具潛力的解決方案。;This thesis introduces a novel modeling framework， the Hierarchical Vector Copula-based first-order Markov process， designed to capture complex dependencies in multidimensional time series data. Traditional copula models often face computational bottlenecks or restrictive assumptions when applied to standard multivariate distributions. To overcome these limitations， we propose a generalized methodology that effectively decouples cross-sectional (spatial) correlations from temporal dependencies. By utilizing mathematical transformation techniques to map dependent variables into independent components， we derive an exact and tractable formulation for the joint density function without relying on restrictive classical forms. For model estimation， we employ a robust hybrid strategy combining Maximum Likelihood Estimation with Inference Functions for Margins to ensure both computational stability and asymptotic efficiency. The mathematical mechanics and practical applicability of the proposed framework are validated through comprehensive simulation studies and empirical analysis of global financial crises. Ultimately， our findings demonstrate that this new architecture provides a robust， flexible， and promising solution for characterizing asymmetric risk contagion and extreme tail movements in multidimensional data.
