- 學位論文
金融風暴後標準普爾500指數於時間序列最適模型之研究
The Application of Time Series model for Standard and poor’s 500 Index after Financial Tsunami.
摘要
本研究期間為2008/1/1~2013/12/31，共313筆週資料，研究對象有S&P500與美元指數、黃金、石油、道瓊歐洲600、及CRB指數，本研究分成兩階段。 第一階段，時間序列方法中，單根檢定，取對數一階差分為定態後，由ARIMA模型、GARCH模型來預測S&P500。經研究實證結果，預測模型比較，由三個誤差判別指標(RMSE、MAE、MAPE)選出，以ARIMA(2,1,2)-GARCH(1,1)為最佳預測模型。 第二階段，觀察S&P500與美元指數、黃金、道瓊歐洲600、石油及CRB指數等模型相互間關係。因考量各模型變數恆定性，經由單根檢定，取對數一階差分後為定態，再由共整合分析、向量誤差修正模型、Granger因果關係檢定、衝擊反應分析、預測誤差變異數分解等方法判定各模型變數相互關係。 經由Johansen共整合分析實證，發現變數模型組合具有長期穩定均衡關係。Granger因果關係檢定，發現黃金單向影響S&P500、道瓊歐洲600及CRB；道瓊歐洲600單向影響石油及CRB；S&P500單向影響CRB；而S&P500和道瓊歐洲600有雙向回饋；黃金和石油有雙向回饋；石油和CRB有雙向回饋，美元指數與各模型皆無領先、落後關係。衝擊反應分析法中，發現被解釋變數受到解釋變數外生衝擊反應後，不管是正向、反向，或長期、短期，皆會在第14期逐漸平緩。預測變異數分解結果，各指數、商品於第1期解釋能力皆為最高，隨期數逐期遞減。第16期時，解釋能力在50%以上有S&500、美元指數、石油及黃金，代表其自我解釋及自發性高，不易受其他商品及指數影響。反觀，道瓊歐洲600、CRB第16期時解釋能力降至50%以下，易受到某些商品、指數有或市場狀況程度影響。綜上所述，金融風暴後，各變數模型因市場流動資金過多，造成非常態景象。
並列摘要
This paper examines the data of 313 sequential weekly samples taking place between 2008/1/1 and 2013/12/31. The data include six variables: S&P 500 index, USD index, Gold index, Oil index, Stoxx Europe 600, and CRB index. This research has been conducted in two phrases. The first phase is to forecast the trend of each variable by adopting ARIMA and GARCH time series models after getting the First Order Difference under Unit Root Test. The model selection result using the minimum error of MAPE has shown that ARIMA(2,1,2)-GARCH(1,1)is the best forecast model for all six variables. The second phase is to study the correlations among S&P 500 index, USD index, Oil index, Gold index, Stoxx Europe 600 and CRB index. Since we have the consistency among six best models, through Unit Root Test, we identify the correlations among underlying models by getting first order difference as stationary then examining the Cointegration test, VECM, Granger causality test, Impulse response Analytics and Forecast Error Variance Decomposition. It is discovered that the variable model combinations have long-term and stable relationships. Granger causality test result shows one-way causality of six pairs; ( gold to S&P 500 index), (gold to Stoxx Europe 600), (gold to CRB index), (Stoxx Europe 600 to oil),( Stoxx Europe 600 to CRB index),and (S&P 500 index to CRB index). Two-way causality is also detected for three pairs (S&P 500 index and Stoxx Europe 600) , (gold and oil), and (CRB index and oil). Additionally, no causality is found between USD index and other five variables. For impulse response analyses, it is discovered that the impact of exogenous factors to response variable stabilizes in 14th period regardless of the long -term, short-term, positive or negative impacts. Forecast Error Variance Decomposition result shows that all variables are with the highest impact in the first-period time and diminish afterwards. In the 16th period, over 50% self-explanatory effect can be found for S&P 500 index, USD index, gold, and oil. For the other two variables(Stoxx Europe 600 and CRB index react), the self-explanatory effect is less than 50% and they are more prone to changes of other instruments or market trends. In summary,, after financial crisis, all models run with different results from those for normal circumstances due to excessive supply of liquid assets.