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題名 | Box-Cox指數轉換之研究及其應用於月流量時序之分析 |
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作者 | 虞國興; 歐立中; | 書刊名 | 農業工程學報 |
卷期 | 39:3 1993.09[民82.09] |
頁次 | 頁53-66 |
分類號 | 443.046 |
關鍵詞 | 月流量; Box-Cox指數轉換; 時序; 非常態時序; 定常性時序; Box-Cox power transformation; Stationary time series; Non-gaussian time series; |
語文 | 中文(Chinese) |
中文摘要 | 水文時間序列上大都為非定常性非常態之時間序列,本研究利用Box and Cox (1964)所提之指數轉換(Power transformation)將序列轉換後再分析其模式,研究中利用由Yu及Lin (1991)所提之部份自迴歸模式(Subset autoregressive model簡稱SAR模式)分別模擬轉換前後之序列。研究結果顯示,無論合成資料或實測資料,Box-Cox所提轉換參數之推估方法均能有效推求轉換參數,然當以非常態分布擾動項產生合成序列時,轉換後模式之擾動項大都無通過常態分布檢定。實測月流量之研究結果發現大部份轉換後模式之擾動項通過常態分布檢定,顯示實測月流量序列大部份仍具備常態分布擾動項,同時,轉換後序列SAR模式於低流量(11-4月)時其預測能力甚佳。本研究依據常態分布之特性,提出另一毋須經過模式模擬之轉換參數推估方法,結果顯示此方法能有效推估轉換參數,且能節省算時間。 |
英文摘要 | Most of the hydrologic time series are non-stationary and non-Gaussion process. The power transformation proposed by Box and Cox (1964) was used to transform the data in the present study. Then, the transformed data were analyzed and fitted the model. In this study, the subset autoregressive model, denoted SAR in brief, proposed by Yu and Lin (1991) was employed to fit the data and its transformed data. The results indicated that method proposed by Box-Cox can estimate the transformation parameter in accuracy. However, the noise term of transformed data could not pass the normality test in general when the series are generated with non-Gaussian noise. When the monthly streamflows were studied. It showed that most of the noise term of the transformed data pass the normality test. This results indicated that most of the observed monthly streamflows contain Gaussian noise terms. Meanwhile, SAR model for transformed data can forecast the low flow (Nov.-Apr.) much better than the SAR model for the original data. Based on the properties of Gaussianity, a methodology for estimating the transformation parameter without modeling the data was proposed in the present study. The results indicated that the proposed method and efficiently estimate the transformation parameter and save lots of computation time. |
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