具狀態轉換之類股與加權指數之誤差修正模型

An Error Correction Model with Regime Switch for TAIEX and Sector Indexes

謝亞芝(Ya-Chih Hsieh)

指導教授 ： 李孟峰

國立臺北大學/商學院/統計學系/碩士(2013年)

摘要

台灣股市各類股與加權指數的漲跌雖然大多存在著齊漲齊跌的現象，但是類股間與加權指數的漲跌幅度並不完全相同，此差異提供了投資者一個轉換類股部位的套利空間。本文利用具有狀態轉換的共整合模型，採用匯率作外生變數建立類股與大盤間的長期均衡關係，並得到一個具有狀態轉換的誤差修正模型。
基於不同類股在長期的情況下具有一個均衡的關係式，但是在短期間可能存在偏離均衡模型的現象。誤差修正模型會使得短期偏離長期均衡的現象漸漸縮小朝向穩定的均衡趨勢，因此投資者可以考慮降低正向偏離過大的類股部位，增加負偏離過大的部位，以藉由誤差修正現象獲得套利的收益。
由於台灣的產業特性，使得匯率對股價具有一定的影響，因此本研究加入匯率作為外生變數。研究發現，誤差修正模型會因股市的空頭及多頭狀態而有所不同，故結合馬可夫狀態轉換的概念，考慮狀態因素所得到之誤差修正模型可以表現在不同狀態之下的均衡關係，將提高誤差修正的精確性。

關鍵字

套利 ； 馬可夫狀態轉換 ； 共整合檢定 ； 向量誤差修正模型

並列摘要

Although the rise and fall of TAIEX and Sector Indexes are usually with the same tendency, the ranges of variation are not alike totally. The difference of variation provides arbitrage for investors. This research establishes a cointegration model with regime switching which also includes exchange (NTD/USD) rate as an exogenous variable to build long term equilibrium among TAIEX, Financial sector, and Electronic sector indexes. An error correction model with regime switching is also derived.
Based on the equilibrium equation, one may find a long term trend among different sector indexes. But in the short term, deviations apart from the equilibrium equation maybe happen. The error correction model will lead the short term deviation towards stable equilibrium gradually. Such correction function provides an arbitrage for investor. The investors can reduce the positions that are positive deviating, and increase the positions that are negative deviating.
Because of the characteristic of Taiwan's industries, exchange rate often influences stock prices some extent, this study then adopts exchange rate as an exogenous variable. According to the finding of this research, error correction models will be influenced by short and long state of stock market. So, error correction models combining the concept of Markov regime switching will improve the accuracy of error correction.

並列關鍵字

Arbitrage ； Markov regime switching ； Cointegration ； Vector error correction model

參考文獻

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