應用MARS與SVR探討小波轉換之基底與階層在財務時間序列預測上之意涵與績效

Evaluating the performance of different wavelet basis functions and levels in forecasting financial time series using MARS and SVR

張智翔(Chih-Hsiang Chang)

指導教授 ： 邱志洲 ； 呂奇傑

國立臺北科技大學/管理學院/商業自動化與管理研究所/碩士(2010年)

摘要

小波轉換(wavelet transform, WT)具有處理時間序列訊號能力，常用在訊號之前處理，可以找出隱藏在時間序列資料中的一些特徵資訊。小波轉換已普遍用於股票市場之預測，但現階段解釋小波轉換之基底函數(Basis Functions)與階層數(Level)在實務上所帶來的意涵之文獻卻很少，而傳統小波轉換也存在解析過後子訊號過多之問題。為了解決此一問題，本研究結合小波轉換、多元適應性雲形迴歸(Multivariate adaptive regression splines, MARS)與支援向量迴歸(Support vector regression, SVR)，建構股價預測模型進行股價指數預測，首先將利用小波轉換中的多尺度解析分析(multi-resolution analysis, MRA)，將預測變數分解出許多不同階層之子訊號，接著將這些分離出來的子訊號當作輸入變數，帶入MARS中作變數篩選。從小波轉換所解析出來的眾多子序號中，以MARS獨特的變數篩選能力，找出影響預測變數裡最重要的輸入變數，最後再將所篩選出來的的輸入變數帶入支援向量迴歸預測器中。在股票市場資料方面以成熟市場美國(DJIA)、日本(N225)及新興市場上海(SSEC)、巴西(BVSP)作為研究之對像，建構模型並對預測變數進行實證研究，進一步探討小波基底函數以及分解階層數在股票市場中所代表之意涵以及實務上之績效。本研究將重點放置於預測變數於實務上之解釋。在實證結果發現，整合模式除了能達到一定之預測水準之外，更能增進模型的附屬價值、減少模型運算時間。並提供在預測未來市場時，使用Daubechies 4小波基底函數能得到最好之預測結果。且預測不同種類市場時，提供應分解之階層數以及所要使用之股價核心訊息。

關鍵字

小波轉換 ； 多元適應性雲型迴歸 ； 支援向量迴歸 ； 股價預測 ； 特徵萃取

並列摘要

Wavelet Transform(WT) has a capability of processing time series signal.WT do preprocess singal in common , it can find some characteristic informations hiding in time series data.Wavelet transfom has used in forecasting market stock already , but there are less literatures in explaining pragmatic means which the Basis Funcation and Levels of Wavelet Transfom work.For solving the question of large varables which Wavelet Tranform has now.In this research a new model which combining Wavelet Transfrom, MARS(Multivariate adaptive regression splines) and SVR(Support vector regression, SVR) is created in forecasting stock market price.Using a capability of Wavelet Transform called multi-resolution analysis(MRA) to decompose origianl signals into many sub-signals .Then put these sub-singals into MARS and fining important sub-signls in forecasting stock price.In this case , these important sub-signals can be inputs in biulding SVR forecasting models.Both mature market data─Amarica market(DJIA) , Japen market(Nikkie225) and Emerging Market data ─ShangHai market(SSEC) , Brazil market(BVSP) are taken for building integrated model.In order to prove benefits of model and explain the performance of different wavelet basis functions and levels in forecasting stock price.This research suggests investors to make a right decision with the high beneficial data.The result tells that intergration model reduce time of biulding model and having a standard in forecasting financial time series.It also brings addible values.The intergration model can provide best basis function of wavelet transform in forecasting financial time sercies which is Daubechies 4.The model also provide which decomposition levels and core stock price of using wavelet transform in forecasting different stock market.

並列關鍵字

Wavelet Transform ； Multivariate adaptive regression splines ； Support vector regression ； Feature extraction ； Stock Forecasting

參考文獻

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