本文研究之目的是採用文獻上較罕見的ARMAX-EGARCH配適動態分配房價指數報酬率，因其考量外生變數，故配適度較佳，並藉由Copula-ARMAX-EGARCH推估大中華地區房市傳染效應之嚴重性。儘管Copula能捕捉任兩區全方面不動產報酬波動的相關性，但當極端事件發生時，Tail dependence 才能有效地掌握尾部相關切確值，有鑑於美國次級房貸對全球經濟的影響甚鉅，了解此區彼此房市間的傳染效應為當務之急。
    實證結果發現大中華地區房市報酬率確實受其本身不同的總體變數所影響，就Copula而言，台灣對香港及台灣對中國皆採用較敏感的Student-T，另外，Tail dependence的Gumbel證實前者在房市繁榮時有相關性，透過橢圓及阿基米德Copula家族估算，此區房市傳染效應皆小於19%，初步推估此區房市有風險分散的效益。

The purpose of this paper fits dynamics distribution housing indices returns estimates the severity of contagion effect across Great China Area real estate markets based on Copula-ARMAX-EGARCH. Although the model is rare in literatures, it provides a better fit due to exogenous variables. Even though Copula could comprehensively capture the correlation of any two real estate volatilities of these areas, it fails once an extreme event outbreaks, but tail dependence could exactly estimate the bilateral degree of correlation in that case. In view of the great influence of U.S. subprime mortgage to global economy, understanding the contagion effects between any two of these areas property markets is urgent.

Content
Abstract:	III
Content	IV
Table Content	V
Figure Content	VI
Chapter 1 Introduction	1
1.1 Background and motivation	1
1.2 Objective	6
1.3 Contribution to the literature	6
1.4 Thesis overview	7
Chapter 2 Theory and Literature	9
2.1 Macroeconomic and real estate market	9
2.2 Literature review	11
Chapter 3 Methodology	22
3.1 ARMAX-EGARCH model	22
3.1.1 ARMAX (m,n) model	23
3.1.2 EGARCH (p,q) model	26
3.1.3 ARMAX(m,d,n)-EGARCH (p,q) model	28
3.2 Copula-ARMAX-EGARCH model	29
3.2.1 Copula model	29
3.2.2 COPULA-ARMAX-EGARCH model	37
3.3 Tail dependence	38
3.4 The conditional probability of contagion effect	39
Chapter 4 Empirical Design and Results Analysis	41
4.1 Data description	41
4.2	Estimation	44
4.2.1 ARMAX(1,0,7)-EGARCH(1,1) model	45
4.2.2 Copula-ARMAX(1,0,7)-EGARCH(1,1) model	51
4.2.3 Tail dependence	55
4.2.4 The conditional probability of contagion effect	57
Chapter 5 Conclusion and Suggestion	64
Reference	67

Table Content
Table 1: Integration of macroeconomic factors for the relevant literatures	13
Table 2: Elliptical copulas’ details and Kendall tau	34
Table 3: Archimedean copulas’ details and Kendall tau 36
Table 4: Tail dependence of three copulas	39
Table 5: Great China Area real estate indices sources	41
Table 6: Great China Area’s real estate indices statistics	42
Table 7: The parametric estimation results of ARMAX(1,0,7) - EGARCH(1,1)	50
Table 8: The Kendall’s tau of copula functions	52
Table 9: Tail dependence of Student-T, Clayton and Gumbel Copula	55
Table 10: Conditional probability of contagion effect for elliptical copulas	60
Table 11: The investment priorities for Great China Area housing markets	61
Table 12: Conditional probability of contagion effect for Clayton & Gumbel Copulas	62
Table 13: Conditional probability of contagion effect for Frank Copula	63

Figure Content
Figure 1: Asian map	5
Figure 2: The flow chart of this thesis	8
Figure 2: Great China Area Real Estate Indices	42
Figure 3: The frequency distribution of the returns of three real estate indices	43
Figure 4: QQ plot for Great China Area indices returns	43
Figure 5: Foreign Direct investment in Taiwan real estate	46
Figure 6: Bilaterally marginal distribution density function of elliptical copulas	53
Figure 7: Bilaterally marginal distribution density function of Archimedean Copulas	56

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