失業率關係到一個國家的經濟而且也受到全球經濟的影響。多維時間序列也被用來處理多個國家之間的失業率。在建立多維時間序列模型的時候，我們應該考慮在每個邊際時間序列之間一個比較彈性的相關結構。近年來，copula模型在高維度的相關結構建模中提供了一個比較彈性的架構。在本篇論文中，我們考慮兩中邊際時間序列，包含white noise 和GARCH。接著，我們用不同的copula去連結這些時間序列，包括有Gaussian copula和三個比較普遍的Archimedean copulas。最後， 我們透過模擬去論證我們的模型以及用台灣日本和美國的失業率去做實例分析。 The unemployment rate is related to the economics of its own country and also influenced by global economics. Multivariate time series are used for modeling unemployment rates among different countries. When modeling multivariate time series, a more flexible dependence structure among each marginal time series should be considered. Recently, the copula model provides a flexible framework for modeling high dimensional dependence structure. In this thesis, we consider two marginal time series, including the simple white noise and the generalized autoregressive conditional heteroskedasticity (GARCH). Then, we merge these time series by a variety of copulas, including the Gaussian copula and three popular Archimedean copulas. Finally, we demonstrate our models through simulation studies and a real data analysis using unemployment rates of Taiwan, Japan, and the United States.
