本論文探討COMEX(美國)及TOCOM(日本)黃金與白銀期貨市場之動態關係，風險值與門檻效果檢定。首先，使用AR (1)-GJR-GARCH(1，1)及三個最常使用的Copula函數被用來檢驗兩個市場之黃金與白銀在上漲前與上漲後的動態關係。另外，使用Coupla基礎的VaR-ARMAX-GJR-GARCH模型被用來檢驗策略商品變數之共移及方向關系並且估計黃金白銀投資組合之風險值。最後使用縱橫平滑轉換迴歸模型(PSTR)檢驗原油與美元/日圓匯率對黃金(白銀)期貨在COMEX市場上的非線性動態關係。控制變數波動指數(VIX)及新興市場指數(MSCI-E)與黃金(白銀)期貨之關係也一併被討論。結果顯示兩個市場的黃金與白銀期貨在上漲前與上漲後存在落後一階顯著的波動外溢與傳遞效果。對於牛市與熊市消息的反應存在不對稱效果。在三個Copula函數中Clayton Copula在上漲前與上漲後最能補捉所有的報酬序列。Clayton Copula Kendall’s tau顯示低度(高度)相關在兩個商品期貨市場中被低(高)平均報酬所驗證在黃金期貨上漲前(後)。另外，原油與COMEX及TOCOM兩個市場的黃金與白銀價格為顯著正相關不管在上漲前或上漲後。至於美金與日元匯率並無一致性的結果，也就是說沒有證據顯示黃金與白銀的期貨存在具有影響性的變數。除此之外，與時俱變的SJC Copula函數允許不同的尾部相關，不管是上漲前或上漲後有最佳的結果。進一步而言，關於風險管理，Copula基礎模型在評估投資組合的風險上較其他模型更正確。最後，實證顯示轉換變數在模型ㄧ與模型三(門檻變數為原油)為非對稱邏輯模型，模型二與模型四(門檻變數為美元/日元匯率)為對稱及指數模型。控制變數的符號隨著門檻變數與區域(regions)不同符號也隨之改變。原油與黃金(白銀)的符號在大部份的區域為正與大部份的文獻相同。美元對日元匯率與黃金(白銀)在大部份的區域為正，此結果與文獻不同且與投資者的認知不一樣。關於VIX與MSCI-E大約有一半的區域為正，暗示投資者在購買黃金與白銀時應該以原油與美元/日元匯率做為重要的指標。

This dissertation discusses the dynamic relationship, value at risk, and threshold effect of gold and silver futures in the markets of COMEX (US) and TOCOM (Japan). First, AR(1)-GJR-GARCH(1,1) and three widely used Copula functions are employed to examine the dynamic relationship of gold and silver futures in above two markets before and during uptrend. In addition, the Copula-based VaR-ARMAX-GJR-GARCH model is used to examine the strategic commodities comovements and directional relationships with these variables, as well as estimating the VaR of a gold and silver portfolio. Finally, the Panel Smooth Transition Regression model (PSTR) is constructed to investigate the nonlinear dynamic relationship between crude oil, USD/YEN exchange rate and gold (silver) futures in COMEX market. Control variables VIX and MSCI-E to the gold (silver) futures are also discussed.  Results show existing spillover effect by one lag both on return and volatility of gold (silver) futures between two markets before (during) uptrend. The responses of bullish and bearish news are asymmetrical in both gold and silver futures of two markets before (during) the uptrend. Clayton Copula model fits all the return series best both before and during uptrend. The Kendall’s tau of the Clayton Copula show low (high) correlation between two commodity futures in two markets. This result is verified by low (high) average return of two commodities across markets before (during) uptrend. The relationships of crude oil and the gold (silver) price in two markets exist significant and positive signs before (during) uptrend. As to USD/YEN exchange rate, there is still no consistent result. There is no evidence that an influence of the variable to gold and silver futures exists. The time-varying SJC Copula, which allows for different dependence in the tails, produced the best result regardless of being before or during uptrend. Furthermore, concerning risk management, Copula-based models are more accurately than other models to assess portfolio risk. The transition function is an asymmetric logistic type in mode 1 and 3 (threshold variable is crude oil), while a symmetric exponential type in model 2 and 4 (threshold variable is the USD). The signs of the control variables are changeable due to the threshold variables and regions. The crude oil is positive in most regions which agree to most literatures. However, USD is positive in most regions which are contrary to previous empirical results and to investors’ common perception.. Lastly, both VIX and MSCI-E are positives in around half of the regions. It suggests that investors should consider crude oil or the USD as crucial indicators for buying gold or silver futures.

Table of Content                                             Page
LIST OF TABLES	                                      VI
LIST OF FIGURES	                                    VIII
CHAPTER 1 INTRODUCTION	                              1
1.1 MOTIVATION	                                       1
1.2 OBJECTIVES	                                       5
1.3 THE FLOW CHART	7
CHAPTER 2 LITERATURE REVIEW                           	  8
CHAPTER 3 METHODOLOGY	                             14
3.1 DATA RESOURCE	14
3.2 COPULA FUNCTIONS AND AR(1)-GJR-GARCH(1,1)	           15
3.3 COPULA-ARMAX-GJR-GARCH BASED VAR MODEL	           20
3.4 PANEL SMOOTH THRESHOLD REGRESSION MODEL	           24
CHAPTER 4 EMPIRICAL RESULTS AND ANALYSIS	           28
4.1 VARIABLES DESCRIPTION STATISTICS     	           28
4.2 THE DYNAMIC RELATIONSHIP	                    31
4.3 THE VALUE AT RISK	                             35
4.4 THE THRESHOLD EFFECT	                             43
4.4.1 Model 1 Gold Future (Threshold variable: Crude Oil)	                                               43
4.4.2 Model 2: Gold Future (Threshold Variable: USD/YEN)	                                               46
4.4.3 Model 3: Silver Future (Threshold variable: Crude Oil)	                                               50
4.4.4 Model 4: Silver Future (Threshold variable: USD/YEN)	                                               54
CHAPTER 5 CONCLUDING AND REMARKS	                    58
5.1 THE DYNAMIC RELATIONSHIP	                    58
5.2 THE VALUE AT RISK	                             58
5.3 THE THRESHOLD EFFECT	                             59
REFERENCES	                                      62


 
LIST OF TABLES
TABLE 3.1.1  DATA RESOURCES USED IN THIS DISSERTATION	 15
TABLE 4.1.1  SUMMARY STATISTICS OF VARIABLES	          31
TABLE 4.2.1   RESULTS FROM THE AR (1) –GJR-GARCH (1, 1) - MODEL-BEFORE UPTREND	                             32
TABLE 4.2.2  THE KENDALL’S TAU OF COPULA FUNCTIONS-BEFORE UPTREND	                                               33
TABLE 4.2.3  RESULTS FROM THE AR (1)–GJR-GARCH (1, 1) MODEL- DURING UPTREND	                             34
TABLE 4.2.4  THE KENDALL’S TAU OF COPULA FUNCTIONS- DURING UPTREND	                                               35
TABLE 4.3.2  THE KENDALL’S TAU OF COPULA FUNCTIONS-BEFORE UPTREND	                                               38
TABLE 4.3.3  VAR OF PORTFOLIO (BEFORE UPTREND)	 38
TABLE 4.3.4  RESULTS FROM THE ARMAX (1)–GJR-GARCH(1,1)- MODEL-DURING THE UPTREND	                             40
TABLE 4.3.6   VAR OF PORTFOLIO (DURING THE UPTREND)	  42
TABLE 4.4.1.1  TEST OF LINEARITY	                    44
TABLE 4.4.1.2  SEQUENCE OF HOMOGENEITY TESTS FOR SELECTING M	                                                44
TABLE 4.4.1.3  TESTING THE NUMBER OF REGIONS: TESTS OF NO REMAINING NON-LINEARITY	                              44
TABLE 4.4.1.4  PARAMETER ESTIMATION RESULTS FOR PSTR MODEL                                                     46
TABLE 4.4.2.1  LINEARITY TESTS	                     47
TABLE 4.4.2.2  SEQUENCE OF HOMOGENEITY TESTS FOR SELECTING M                                                        47 	                                                  TABLE 4.4.2.3  TESTING THE NUMBER OF REGIONS: TESTS OF NO REMAINING NON-LINEARITY	                             48
TABLE 4.4.2.4  PARAMETER ESTIMATION RESULTS FOR PANEL SMOOTH TRANSITION REGRESSION (PSTR) MODEL	           49
TABLE 4.4.3.1  LINEARITY TESTS	                    51
TABLE 4.4.3.2  SEQUENCE OF HOMOGENEITY TESTS FOR SELECTING M	                                               51
TABLE 4.4.3.4  PARAMETER ESTIMATION RESULTS FOR PSTR MODEL	                                               53
TABLE 4.4.4.1  LINEARITY TESTS	                    55
TABLE 4.4.4.2  LINEARITY TESTS	                    55
TABLE 4.4.4.3  TESTING THE NUMBER OF REGIONS: TESTS OF NO REMAINING NON-LINEARITY	                              55
TABLE 4.4.4.4  PARAMETER ESTIMATION RESULTS FOR PSTR MODEL	                                                57


 
LIST OF FIGURES
FIGUE 1.1 COMPARISION OF MSCI-E AND ECONOMIST METAL INDEX……………..,…                               .      4
FIGUE 1.3.1 FLOW CHART                                    7
FIGURE 4.1.1 THE PRICE TREND OF COMEX AND TOCOM GOLD FUTURES	                                                29
FIGURE 4.1.2 THE RETURNS TREND OF GOLD AND SILVER FUTURES IN TWO MARKETS	                                       29
FIGURE 4.1.3 THE TIME SERIES PLOT OF VARIABLES	  30
FIGURE 4.1.4 THE HISTOGRAM WITH NORMAL CURVE OF COMEX AND TOCOM GOLD FUTURES RETURN	                              30
FIGURE 4.1.5 THE HISTOGRAM WITH NORMAL CURVE OF COMEX AND TOCOM SILVER FUTURES RETURN	                              30
FIGURE 4.2.1 SCATTER PLOT OF COMEXGOLD AND TOCOMGOLD (LEFT), COMEXSILVER AND TOCOMSILVER	                     33
FIGURE 4.2.2 SCATTER PLOT OF COMEXGOLD AND TOCOMGOLD (LEFT),COMEXSILVER AND TOCOMSILVER	                     35
FIGURE 4.3.1 THE CRUDE OIL AND USD/YEN TREND	            36
FIGURE 4.3.2 THE TIME VARYING JOE-CLAYTON TAU	            39
FIGURE 4.3.3: PVAR AT 99%.97.5%,95% CONFIDENCE LEVEL-VAR-COV MODEL	                                                39
FIGURE 4.3.4 THE TIME VARYING JOE-CLAYTON TAU	           42
FIGURE4.3.5 : PVAR AT 99%.97.5%,95% CONFIDENCE LEVEL-VAR-COV MODEL	                                                42
FIGURE 4.4.1.1 TRANSITION FUNCTION WITH M = 1	           46
FIGURE 4.4.2.1 TRANSITION FUNCTION WITH M = 2 	  50
FIGURE 4.4.3.1: TRANSITION FUNCTION WITH M = 1	  54
FIGURE 4.4.4.1: TRANSITION FUNCTION WITH M = 2	  57

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