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

Forecasting Corn Future Prices with Markov Switching Model and GARCH Type Time Series Model

陳盈君(Ying-Chun Chen)

指導教授 ： 許玉雪

國立臺北大學/商學院/統計學系/碩士(2012年)

摘要

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。

關鍵字

時間數列,ARFIMA,Markov switching model(MS),EGARCH,FIGARCH,價格預測,玉米期貨價格

並列摘要

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.

並列關鍵字

Time series, Markov switching model, EGARCH, FIEGARCH, ARFIMA, Price forecasting, Corn Future prices.

參考文獻

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