赫斯特現象意義之探討

Abstract

本文基於時序列為平穩型之前題，根據分式高斯噪音理論並配合計算機模擬，測 試一些不同統計性質的時序列資料，藉以探討滿足赫斯特定律之赫斯特現象所代表的意義。 本文另分析短記憶長度之時序列資料，探討轉線情況之統計特性。研究結果顯示轉線情況亦 表示時序列有持續性，故較完整赫斯特現象之意義應從兩方面加以說明，一為滿足赫斯特定 律者，其意義包含時序列具有長期持續性、特殊自相關函數結構及碎形特徵，三為呈現轉線 情況者，其意義僅表示時序列具持續性或屬短記憶長度性質。Based on the assumptions of a stationary time series and Fractional Gaussian Noises, tests of several generated time series of various statistical properties Were carried out to investigate the meaning of the Hurst phenomenon of satisfying Hurst law. Time series with short memory were also analyzed for exploring statistical characteristics of the cross-over situation. It is found that the crossover situation also represents time series with persistence. The present analysis shows that a full explanation of the Hurst phenomenon should be described by two different ways. One satisfies the Hurst law and represents time series with long-run persistence, special auto-correlation function, and Fractal characteristics. The other one exhibits the crossover situation and represents time series only with persistence or shorr memory.