一個二階段混合式模糊時間序列預測模型

Abstract

模糊時間序列將模糊理論運用在時間序列之預測問題上，其應用模糊邏輯推理，可以補充傳統時間序列於處理模糊及不確定環境下語意資料的不足。在許多被提出的模糊時間序列中，一階模糊時間序列為代表性模型之一，許多基於一階模糊時間序列的改良紛紛被提出，其中包含了啟發式模糊時間序列，其在一階模糊時間序列解模糊步驟中加入預測目標時間序列知識，大幅提升預測準確性。但是該研究中預測目標時間序列知識來自於事先建立的知識庫，無法動態即時更新。針對一個包含預測目標時間序列與輔助時間序列的多時間序列環境中，本研究提出一個二階段混合式模糊時間序列模型，使用輔助時間序列預測結果作為預測目標時間序列知識的來源。模型第一階段是模糊化，建立目標時間序列與輔助時間序列各自的模糊邏輯群。第二階段是解模糊化，將先對輔助時間序列解模糊化，再利用其結果輔助目標時間序列解模糊化，最終得到目標時間序列預測值。本研究參考人工產生的時間序列資料集與近年台幣匯率賣價逐週與逐日歷史資料之趨勢，來驗證提出模型之有效性。模擬結果與一階模糊時間序列預測結果相比，人工產生資料集一預測結果Mean-Square-Error (MSE)減少50.55%，人工產生資料集二預測結果MSE減少18.82%，匯率預逐週趨勢預測結果MSE減少58.11%，逐日趨勢預測結果MSE減少39.56%。模擬結果證實提出的二階段混合式模糊時間序列模型利用輔助時間序列預測結果的確能有效提升目標時間序列預測準確性。

Fuzzy time series models apply fuzzy logic to time series forecasting problems. In an uncertain environment, fuzzy logic can be used to handle deficiencies of traditional time series models in dealing with linguistic variables. In existing research articles, the first-order fuzzy time series (FOFTS) model is the most popular one. Variations of the FOFTS model have been investigated. The heuristic fuzzy time series (HFTS) model is one of these variations. The HFTS model incorporates the knowledge of forecasting targets to the FOFTS model to enhance forecasting accuracy. But the knowledge is most likely from a pre-defined knowledge base, which is usually unable to reflect the real-time environment. In this thesis, a two-phase hybrid fuzzy time series (TPHFTS) model is proposed. The TPHFTS model considers two time series, forecasting targets and auxiliary. The results of auxiliary time series are used as the source of knowledge of forecasting target. In the first phase, the TPHFTS model performs fuzzification and establishes time series with respect to fuzzy logic groups. In the second phase, the TPHFTS model performs defuzzification. The TPHFTS model first defuzzifies auxiliary time series, and subsequently use the results to assist forecasting target in its defuzzification. To verify the proposed model, both daily and weekly exchange rates of new Taiwan dollar (NTD) and two manually generated time series are considered. By comparing to the FOFTS model, we notice that the Mean-Square-Error (MSE) decreases by 50.55% in the first manually generated time series and 18.82% in the second manually generated time series. Also, the simulation results of exchange rate of NTD show the MSE decreases by 39.56% in daily exchange rate and 58.11% in weekly exchange rate. In all respects, the TPHFTS model does improve forecasting accuracy.