本文將模糊理論的觀念，應用在估計、檢定及時間數列分析上。研究重點包括離散型及連續型模糊樣本的定義與度量，模糊參數的最佳估計，模糊排序方法應用於無母數檢定，模糊相似度的定義、性質，以及如何將其應用於辨識不同時間數列間的落差l期相似程度等。我們首先將常見的模糊資料分為離散型及連續型，並針對不同類型的資料，給定對應的模糊平均數、模糊變異數等模糊參數的概念與一些重要性質。接著我們提出幾種估計方法，針對不同的模糊參數進行最佳估計並提出可行的評判準則。進一步地，我們將模糊排序方法應用於無母數檢定推論。最後我們提出模糊相似度的定義與度量。經由系統性的模擬與分析，我們建立兩時間數列間模糊相似度演算法則。實證分析方面，我們利用提出的方法對台灣的股價加權指數、個股股價進行估計及檢定；同時，針對台灣歷年GDP、民間消費、毛投資間的相似性進行偵測，以驗證我們提出的模糊參數估計、模糊無母數檢定及模糊相似度演算法的效率性與實用性。 / In this paper, we apply fuzzy theory in estimation, nonparametric test, and time series analysis. Our focus is on: How to define and measure the discrete type fuzzy data and continuous one? How to find the optimal estimators for fuzzy parameters? How to apply fuzzy ranking methods in nonparametric test when the data is vague? How to define and find the degree of fuzzy similarity between two time series? First, fuzzy data is classified according to its type, discrete or continuous. Then we give some definitions and properties on fuzzy mean, fuzzy variance for different type of fuzzy data. Next, we proposed some estimating methods and evaluation rules. Moreover we apply fuzzy ranking methods in nonparametric test, such as Sign test, Wilcoxon signed rank test, Wilcoxon rank sum test, and so on. Finally, we suggest the definitions as well as the algorithm for computing the degree of fuzzy similarity between two time series. We also give some simulate and empirical examples to illustrate the techniques and to analyze fuzzy data. Results show that fuzzy statistics with soft computing are more realistic and reasonable for the social science research.
| Identifer | oai:union.ndltd.org:CHENGCHI/G0883545052 |
| Creators | 張建瑋, Chang ,Chien-Wei |
| Publisher | 國立政治大學 |
| Source Sets | National Chengchi University Libraries |
| Language | 中文 |
| Detected Language | English |
| Type | text |
| Rights | Copyright © nccu library on behalf of the copyright holders |
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