應用XCSR與XCS於台灣加權股價指數預測之比較

Abstract

真實世界的環境中存在了許多以實數為基礎的問題，包括了資料探勘、參數最佳化、與時間序列的預測等。然而許多過去發展的機器學習方法學卻著重於探索二元(binary)的解空間，當這些方法學被用來解決上述問題時，問題中的實數變數勢必要經過某些前處理的步驟，來對映至二元的解空間。然而將實數對映至二元字串(bitstring)，將會面臨下列問題：包括了精確度的喪失、前處理方式是否適當、固定的前處理方式無法適應不同情況、與計算時間成本增加等。

為了解決上述問題，許多能直接探索實數解空間的方法學也因此被提出，例如演化策略(Evolution Strategies)、模糊邏輯(Fuzzy Logic)等。而某些原本以搜尋二元解空間為主的方法學，也因此修改成實數的學習方式，例如實數基因演算法(Real-Coded Genetic Algorithms)、實數延伸型分類元系統(XCS with Real inputs)等。

時間序列預測的問題處於實數、具有雜訊、複雜、狀態不確定(non-stationary)等特性的解空間中，若是模型無法分辨時間序列中不同的狀態，或許會導致預測能力的下降。因此本研究比較XCSR與XCS於台灣加權股價指數的預測結果，來探討以實數或是二元為基礎的模型，在面對實數解空間時的學習能力。兩種XCS模型的預測結果也分別與買進持有策略與隨機交易策略比較，以驗證模型在實務上的可行性。

實驗結果顯示，可處理實數解空間的XCSR模型不論是在訓練期或是測試期，表現結果均顯著優於XCS模型，而XCS模型又較買進持有與隨機交易策略為優。由實驗結果可得以下結論：二元字串不足以表達實數變數、XCSR較XCS模型更適用於股市之預測。

Many real-world applications involve continuous variables, such as data mining, function optimization, time series forecasting, and so on. However, most previously developed machine learning techniques focus on discovering binary solution spaces. While those techniques are applied to the mentioned applications, the continuous variables have to be preprocess to map onto binary solution spaces. Nevertheless, the mapping process would cause some problems, such as the loss of precision, the inadequacy of preprocess, no adaption to different situations, and the increase of computational time.

In order to conquer those problems, some techniques with abilities to explore continuous solution spaces are devised, such as evolution strategies(ES), fuzzy logics, and so on. Besides, some techniques originally developed for binary solution spaces are modified to deal with continuous variables, such as real-coded genetic algorithms (RCGA), XCS with real inputs(XCSR), and so on.

Time series forecasting is one of the applications with continuous, noisy, complex, non-stationary solution spaces. If the techniques aren’t able to distinguish different states in time series, the forecasting performance may be poor. Therefore the forecasting performance of two kind of XCS, XCSR and XCS, are compared with each other to reveal the difference of continuous and binary based techniques while continuous solution spaces are addressed.

As illustrated in experiments, XCSR performs better than XCS in both training and testing periods, and XCS performs better than “buy and hold” and “random walk” strategies. In conclusion, binary based techniques are insufficient for continuous solution spaces, and XCSR is more applicable than XCS in time series applications.