以離散信號技術探討台灣證券市場循環週期之特性及應用

Abstract

效率市場假說認定資產價格呈現隨機走勢進而否定技術分析之實用性，然而許多針對投資市場的實證研究顯示效率市場假說無法全盤解釋投資人的行為模式，股價並非全然隨機，諸多反證暗示適當的交易策略可賺取超額報酬。景氣循環(Business cycle) 是經濟體系中一個十分明顯而且重要的總體現象。學術上的研究顯示資產價格之循環週期特性和經濟體系中之景氣循環現象密切相關，由於循環具有行為重覆的特性，故資產價格具有某種程度的可預測性。 景氣循環之研究大多著重於循環週期之存在與否及其相關現象之探討，至於實際應用於資產價格之分析與交易的相關研究則付之闕如。本研究嘗試定量分析資產價格的循環週期特性，並據以擬定交易策略挑戰效率市場假說之買進持有策略。利用加法原則、倍數原則及同步原則等週期特性配合頻譜分析(Spectrum analysis)及離散時間(discrete time)信號處理技術等數學工具，分析組成資產價格之成份週期波之週期長度及相位(phase)，進而探討週期分析應用在市場交易之可行性。本研究以台灣加權股價指數為研究對象，樣本期間分為週期模型建立期間及交易測試期間。週期模型建立之資料期間從1987年2月到1999年12月，交易測試期間從2000年1月1日到2010年12月31日，資料取自於台灣經濟新報資料庫。 本研究之分析方法用於台灣加權股價指數模擬交易之年化報酬率為19.6%，顯著優於同時期之買進持有策略的年化報酬率0.34%。

The efficient markets hypoth¬esis (EMH) states that stock prices already reflect all information and accordingly follow a random walk. This statement asserts that trend analysis by examining market trading data such as the history of past prices, trading volume, or short interest is fruitless. Nevertheless discoveries of the relationships that can be used to earn abnormal returns, which violate the EMH are numerous in the finance literature. The business cycle is an important phenomenon observed in macroeconomic time-series data. The close relationship between stock market and macroeconomic implies that the cycle phenomena exists in the stock market as well. This makes the stock prices semi-predictable due to the recurring feature of cycle. This thesis focuses on the study of the cycle phenomena of the stock market and the application of cycle principles in forecasting stock market prices. A simple cyclic model is adopted to develop the trading strategy based on the empirical principles from cyclicality in price motion. The performance of this strategy is compared against that of the buy-and-hold strategy, which is implied as optimal by the EMH. The spectrum analysis is employed to identify the dominant cycle of the time series to be analyzed and the corresponding phase information is defined by discrete-time signal processing technique. The derived cyclic model is then employed to make trading decision. The data used in the study are obtained from TEJ database. The data period used for the cyclic model built-up runs from February 1987 to December 1999 and the data set for trading simulation covers the horizon from January 2000 to December 2010. The proposed trading strategy developed based on the cycle principles provides the annualized return of 19.6%, compared against the annualized return of 0.34% from the buy-and-hold strategy.