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研究生:陳盈君
研究生(外文):Chen, Ying Chun
論文名稱:馬可夫狀態轉換模式與GARCH族群時間數列模式之預測比較分析--玉米期貨價格之實證研究
論文名稱(外文):Forecasting Corn Future Prices with Markov Switching Model and GARCH Type Time Series Model
指導教授:許玉雪許玉雪引用關係
指導教授(外文):Hsu, Esher
口試委員:林金龍李孟峰許玉雪
口試委員(外文):Lin , Jin-LungLee,Mong-HongHsu, Esher
口試日期:2012-07-02
學位類別:碩士
校院名稱:國立臺北大學
系所名稱:統計學系
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:94
中文關鍵詞:時間數列價格預測玉米期貨價格ARFIMAMarkov switching model(MS)EGARCHFIGARCH
外文關鍵詞:ARFIMAMarkov switching model(MS)EGARCHFIGARCHTime seriesPrice forecastingCorn Future prices
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本文旨在探討具狀態改變及依時變動波動度的時間序列資料之預測模式,比較分析這些模式的配適能力。玉米是飼料作物亦是能源作物,影響民生至大,近幾年玉米期貨價格波動劇烈,自2008年爆發糧食危機後玉米期貨價格波幅變大,高價格變化產生數列的狀態轉變,但2008年前玉米價格仍保有高度平穩的持續性,故時間數列的特性隱含長期記憶性、依時變動的波動性、及狀態轉換的特性,不易預測。故本文以玉米期貨價格為例,透過實證分析及Monte Carlo模擬法,試圖找出具長期記憶性、數列波動性、及狀態轉換特性的時間序列資料之較佳預測模式。
首先,以玉米期貨價格進行實證分析,分別討論長期記憶性、依時變動的波動性、具狀態轉換的時間數列預測模式,進行配適與預測以找出玉米期貨價格較佳的配適模型,做為模擬母體模式的基礎。根據實證結果發現,馬可夫狀態轉換模式(MS-ARMA)、依時變動的波動度TGARCH-ARMA模式、長期記憶性ARFIMA模式對玉米期貨價格的配適及預測能力較佳。故本文以此三個模式為基礎,利用蒙地卡羅研究法模擬六種不同母體模式下的時間序列資料,分別配適單變量ARFIMA、TGARCH-ARMA、EGARCH-ARMA、MS-ARMA四個模式,並比較分析這四個模式對來自六種不同母體模式下的時間序列資料配適能力。
模擬分析結果發現:(1)馬可夫動態模式MS(2)-ARMA(1,1)不僅能準確評估數列的狀態轉換,亦可捕捉長期記憶性質,映證楊雅瑜 (2007)認為MS能捕捉ARFIMA之特性;(2)且研究發現馬可夫狀態轉換模式亦能捕捉依時變動的波動度模式之槓桿效應;(3)不管時間序列資料來自馬可夫狀態轉換模式(MS-ARMA)、依時變動的波動度的TGARCH-ARMA模式、或長期記憶ARFIMA模式,MS(2)-ARMA都有很好的配適能力;(4)模擬結果亦發現大樣本能有效降低預測結果之均方根誤差(RMSE),提升時間數列的配適能力。綜合研究結果除了顯示馬可夫動態模式適合做為玉米期貨價格之預測模式,亦發現馬可夫動態模式適用於具長期記憶性、數列波動性、具狀態轉換的非線性時間數列之預測,並可應用到其他農產品期貨價格預測上。

This thesis aims to conduct a comparative analysis on the forecast performance of Markov Switching Model and GARCH Type Time Series Model. Maize, not only used for feeding stuff of livestock, but also used for biomass energy, is an important agricultural crop. Recently, the corn future prices have large fluctuation. Corn prices retained a high degree of stable continuity of its time series characteristics before 2008, which implied the characteristic of long memory. The food crisis broken out in 2008 has enlarged the price volatility of corn, which further resulted in high-price changes in time series and implied the state transition. The time series with the characteristics of large series volatility and regime switching is difficult to predict. In this study, corn future prices is used as an example to explore prediction models for time series data with characteristic of state changes and long memory. Empirical analysis and Monte Carlo simulation method are used in this study to find a better prediction model for the time series data.
First, an empirical analysis is conducted on corn future prices. Prediction models with the integrated characteristics of long memory, time-varying volatility, and regime switching are used for data fitting and prediction. The better-fitting models carried out by the empirical analysis are used as the basis of the population models of time series with long memory, series volatility, and state transitions. The empirical results show that the Markov switching model (MS-ARMA), TGARCH-ARMA model, and ARFIMA model provide good fit for corn future prices. Six different models derived from those three models are then used as population models for Monte Carlo approach. The ARFIMA, TGARCH-ARMA, EGARCH -ARMA, and MS-ARMA are used to fit the time series data generated from the six population models.
The simulation results showed that (1) MS(2)-ARMA(1,1) could not only fit the series pattern of state transitions nature, but also capture the nature of long memory which also illustrate the study results from Yang(2007) that the MS can catch the features of ARFIMA, (2) Markov switching model can also capture the leverage effect of time-varying volatility, (3) The Markov MS(2)- ARMA has a good fitting for the time series data from the populations with Markov switching (MS- ARMA), TGARCH- ARMA or ARFIMA model, (4) The simulation results also found that large sample can effectively reduce the root mean square error (RMSE) of prediction. In general, the study results show that Markov switching model is a good model to catch the series pattern of corn future prices. This study results suggest that Markov switching model is suitable for the time series data with long memory, time-varying volatility, and state transitions. The study results can also be applied for future price forecasts of other grains.

目錄
目錄 v
圖目錄 vii
表目錄 viii
第 1 章 緒論 1
1.1. 研究動機與目的 1
1.2. 研究架構 5
第 2 章 文獻回顧 7
2.1. 長期記憶模型 7
2.2. ARCH-GARCH模式 10
2.3. 馬克夫狀態轉換模型 12
2.4. 農產品期貨價格預測相關文獻回顧 16
2.5. 小結 18
第 3 章 研究方法 19
3.1 研究流程 19
3.2 ARFIMA 模式及其特性 20
3.2.1 ARFIMA 模式參數估計 22
3.2.2 ARFIMA 模式的白噪音性質及單根檢定 23
3.3 GARCH模式及其擴展 27
3.3.1 具槓桿效果與不對稱性的GARCH 30
3.3.2 具長期記憶性的FIGARCH 31
3.4 Markov-Switching模式 33
3.5 模式評估準則 36
3.5.1 樣本內模型配適 37
3.5.2 樣本外模式預測 38
第 4 章 實證分析結果 41
4.1 玉米期貨價格分析 43
4.1.1 玉米商品期貨的功能與影響 43
4.1.2 歷年玉米期貨價格之變動 46
4.1.3 玉米期貨價格之敘述統計 48
4.2 實證結果分析 50
4.2.1 模型配適結果 52
4.2.2 實證結果綜合分析 68
第 5 章 蒙地卡羅模擬分析 71
5.1 MS(2)-ARMA(1,1) 模式的模擬結果 75
5.2 TGARCH(1,1)-ARMA(1,1)模式的模擬結果 78
5.3 ARFIMA(1,d,1) 模式的模擬結果 80
5.4 模擬結果綜合分析 81
第 6 章 結論與建議 83
6.1 研究結論 83
6.2 研究建議 85
參考文獻 86
附錄 A: 原始資料 91


圖目錄
圖 ‎1 1 研究流程圖 6
圖 ‎4 1 實證流程圖 42
圖 ‎4 2 1992~2011年間玉米期貨價格重大轉折點 47
圖 ‎4 3 玉米期貨原始價格的ACF 50
圖 ‎4 4 差分一次後的玉米期貨價格 51
圖 ‎4 5 ARFIMA(1,d,1)配適情形及殘差與常態的比較 54
圖 ‎4 6 ARFIMA(1,d,2)配適情形及殘差與常態的比較 54
圖 ‎4 7 ARFIMA(1,d,1)及ARFIMA(1,d,2)的後六期預測能力 55
圖 ‎4 8 TGARCH(1,1)-ARMA(1,1)-G的配適模型 61
圖 ‎4 9 TGARCH(1,1)-ARMA(1,1)-G的波動度 62
圖 ‎4 10 TGARCH(1,1)-ARMA(1,1)-t的配適模型 62
圖 ‎4 11 TGARCH(1,1)-ARMA(1,1)-t的波動度 62
圖 ‎4 12 TGARCH(1,1)-ARMA(1,1)-G及TGARCH(1,1)-ARMA(1,1)-t的預測 63
圖 ‎4 13 MS(2)-ARMA(1,1)的配適模型 67
圖 ‎4 14 MS(2)-ARMA(1,1)的後六期預測評估 67
圖 ‎5 1 模擬過程流程圖 73


表目錄
表 ‎3 1 ARMA和ARFIMA模式的比較 22
表 ‎3 2 ARFIMA及FIGARCH長期記憶參數的表現 32
表 ‎3 3 ACF及PACF比較 37
表 ‎4 1 CBOT玉米期貨契約 45
表 ‎4 2 玉米期貨的基本敘述統計量 49
表 ‎4 3 玉米期貨價格的單根檢定 51
表 ‎4 4 ARFIMA模型配適的參數估計 52
表 ‎4 5 ARFIMA模式樣本內及樣本外預測能力評估 56
表 ‎4 6 玉米期貨價格的ARCH效果 57
表 ‎4 7 GARCH族群之參數估計 58
表 ‎4 8 玉米期貨價格一階差分後配適模式的診斷 60
表 ‎4 9 玉米期貨在GARCH族群配適模式樣本內及樣本外預測能力評估 61
表 ‎4 10 玉米期貨價格在FIGARCH模式配適下的參數估計 64
表 ‎4 11 玉米期貨價格在FIGARCH配適模式的診斷 64
表 ‎4 12 玉米期貨價格在FIGARCH-AR模式下的預測能力評估 65
表 ‎4 13 玉米期貨價格在馬可夫狀態轉換模型的參數估計 66
表 ‎4 14 玉米期貨在MS配適模式的診斷 66
表 ‎4 15 玉米期貨價配適模型的比較 68
表 ‎4 16 玉米期貨價格的預測能力評估 70
表 ‎5 1 不同樣本觀察值下的玉米期貨價格之模擬資料格式 74
表 ‎5 2 母模式為MS(2)-ARMA(1,1), 之預測結果 75
表 ‎5 3 母模式為MS(2)-ARMA(1,1), 之預測結果 76
表 ‎5 4 母模式為MS(2)-ARMA(1,1), 之預測結果 77
表 ‎5 5 母模式為TGARCH(1,1)- ARMA(1,1)-G之模擬結果 79
表 ‎5 6 母模式為TGARCH(1,1)- ARMA(1,1)-t之預測結果 79
表 ‎5 7 母模式為ARFIMA(1,d,1)之預測結果 81

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