波羅地海指數非線性混沌行為之研究

The Study of Nonlinear Chaotic Behavior–A Perspective of Baltic Dry Index

柯家哲(Chia-Che Ko)

指導教授 ： 胡為善

中原大學/商學院/企業管理學系/碩士(2008年)

https://doi.org/10.6840/cycu200800445

摘要

過去30年來，非線性動態系統如混沌理論已吸引越來越多經濟學者和財金學者的注意，非線性動態系統受青睞的原因主要是因為其對於金融市場上的劇烈波動有很強的解釋能力。目前已經有相當多的研究聚焦於金融市場的波動上，其中，最著名的解釋便是「金融市場是由決定性混沌所支配」。
隨著波羅地海指數(Baltic Dry Index; BDI)突破一萬點且創下歷史新高之際，波羅地海指數吸引了許多的學者的關注。本研究利用Brock, Dechert and Scheinkman (BDS)測試法、Rescaled range (R/S)分析法，以及相關維度等方法測試波羅地海指數的混沌現象。
實證結果證實波羅地海指數具有混沌現象，波羅地海指數為碎型，為一長期記憶的過程(long memory process)及決定性混沌(deterministic chaos)，這也意味傳統的線性分析方法無法有效分析波羅地海指數；實證結果也顯示R/S分析法在有噪音的情況下為一強化的分析方法，此結果與Peters(1996)一致。

關鍵字

波羅地海指數 ； R/S分析法 ； BDS測試法 ； 混沌 ； 相關維度

並列摘要

During the past three decades, nonlinear dynamics system, such as Chaos theory, has captured much attention from economists and financial academics. The nonlinear dynamics system is popular mainly because of its great explanatory power of dramatic movement in financial markets. There have been abundant academic researches focusing on the fluctuations of the financial markets since 1980’s. The well-known illustration is that the financial market is dominated by “Deterministic chaos’’.
As the Baltic Dry Index (BDI) made a breakthrough of ten thousand points and hits the historical height, the BDI was also attracted much attention by the academics. This study attempts to utilize the Brock, Dechert and Scheinkman (BDS) test, Rescaled Range (R/S) analysis, and correlation dimension method to examine whether the BDI has chaotic phenomenon or not.
The empirical results indicate that BDI has chaotic phenomenon, the underlying data of the BDI is fractal, characterized as long memory processes and deterministic chaos, suggesting that the conventional linear methods failed to analyze the BDI. This work results also finds showed that the R/S analysis is a robust method even under the circumstance of noise, which confirms with the finding of Peters (1994).

並列關鍵字

BDS test ； Baltic Dry Index (BDI) ； R/S analysis ； chaos ； correlation dimension

參考文獻

Huang, Huan-Chung, “A Research of Nonlinear Chaos in the Futures Market” Graduate School of Business Administration, Taipei University, Taiwan. (In Chinese)

Peng, Kang-Lan (2003), “Nonlinear Chaotic Behavior in Taiwanese Stock Market” a MBA dissertation of National Taipei University.

Abhyankar, A., Copeland, L. S. and Wong, W (1995), “Nonlinear Dynamics in Real-Time Equity Market Indices: Evidence from the United Kingdom” The Economic Journal, Vol. 105, No. 431, pp. 864-880.

Abhyankar, A., Copeland, L. S. and Wong, W. (1997) “Uncovering Nonlinear Structure in Real-Time Stock-Market indexes: The S&P 500, the DAX, the Nikkei 225, and the FTSE-100” Journal of Business and Economics Statistics, Vol.15, pp. 1-14

Alligood, K.T., Sauer, T.D. and Yorke, J.A. (1996), “Chaos: An Introduction to Dynamical Systems” Springer Verlag, NY.