應用模糊理論於具離群值之時間序列參數的估計及預測

Appling fuzzy theory in estimation and forecasting for time series with outliers

陳鴻元(Hung-Yuan Chen)

指導教授 ： 張建瑋

大同大學/電機資訊學院/應用數學學系所/碩士(2011年)

摘要

Tanaka et al.曾於1982年提出模糊迴歸分析的論點，認為觀測值與估計值的殘差是來自於參數的不確定性，而後續也有許多研究指出模糊迴歸分析對於處理具相關性之不確定性資料確實有相當助益。考量時間序列資料具高度自我相關性及不確定性，故將模糊理論應用於時間序列模式參數之估計似為一可行之方法。
　　此外，由於所蒐集資料中常存在離群值，而離群值對於模式參數之估計常會造成一定程度的影響，故找尋一較具穩健性之估計方法遂成為本文另一研究重點。而由過去的研究文獻顯示，應用模糊理論於參數估計，不但具穩健性，亦能解決資料本身具模糊性及不確定性所造成的估計困難。
　　本研究將模糊群聚分類的概念應用於具離群值之時間序列模型建構，視模式參數為模糊數，並針對此種參數提出模糊加權最小平方估計演算法則來估計參數。同時，我們也將此估計方法與一般傳統時間序列參數之估計方法作比較，以了解所建構模式的預測準確度

關鍵字

模糊理論 ； 最小平方法 ； 估計 ； 時間序列 ； 模糊分類 ； 模糊加權最小平方法

並列摘要

In 1982, Tanaka et al. put forth an argument regarding the fuzzy regression model, and he suggested that the residuals between an observed value and an estimated value result from uncertainty of the parameters. Plenty subsequent studies indicate that the fuzzy regression model is conducive to the processing of correlated uncertain data. Considering that time series data are characterized by high self-correlation and uncertainty, it is feasible to apply fuzzy theory in the estimation of parameters of a time series model.
　　Outliers abound in data gathered. The effect of outliers on the estimation of parameters of a model is seldom negligible. Hence, another objective of this study is to look for a robust estimation method. Many researches pointed out that the application of fuzzy theory in parameter estimation is robust and effective in eliminating estimation difficulties which might otherwise arise from fuzziness and uncertainty of data.
　　This study involves applying the concept of fuzzy clustering in the construction of a time series model, treating parameters of model as fuzzy numbers, and estimating the parameters with an estimation algorithm created by fuzzy weighted least squares.
　We also give some simulate and empirical examples to illustrate the techniques and to analyze fuzzy data. Results show that the methods proposed by us are more realistic and reasonable for the time series data with outliers

並列關鍵字

fuzzy classification ； fuzzy theory ； least squares ； estimation ； Time series ； fuzzy weighted least squares

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