記憶性k-Factor GARMA模式之研究

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Title:	記憶性k-Factor GARMA模式之研究
Authors:	虞國興;何琮裕
Contributors:	淡江大學水資源及環境工程學系
Keywords:	長記憶性過程;GARMA模式;近似最大概似法;Long memory process;Gegenbauer ARMA models;Approximate maximum likelihood method
Date:	2000-12-01
Issue Date:	2009-03-19 14:19:16 (UTC+8)
Publisher:	中國農業工程學會
Abstract:	以往在長記憶水文時序之分析上，常利用差分、除勢等轉換方法。近年來，研究顯示k-factor GARMA模式在長記憶時間序列上有著不錯的預測結果。本研究主要探討此一模式之適用性，並將其應用於臺灣河川月流量資料上，與傳統除勢模式做一比較。本研究於k-factor GARMA模式之參數推估上，採用Hosking(1984)所提出之近似最大概似法；至於模式之判定上本研究則採用AIC、BIC兩種判斷準則。另外，為瞭解模式預測能力之優劣，本研究分別採用MSE、MAPE及UI三種預測指標。研究結果顯示，於合成資料之參數推估上，近似最大概似法受到樣本數的影響較大，在大樣本時可得較高之準確性；而於模式判定方面，受到模式參數與樣本數之影響，整體而言BIC之偵測能力明顯優於AIC。於實測資料分析上，就統計特性保存能力方面，k-factor GARMA模式於偏態係數之保存能力優於除勢模式；除勢模式則於平均值及變異數之表現上較佳，另於預測能力表現上，k-factor GARMA模式於低流量部份之預測能力明顯優於除勢模式。整體而言，k-factor GARMA模式於預測能力上優於傳統除勢模式，且可改善除勢模式無法掌握之偏態保存能力，加上參數精簡原則之考慮，k-factor GARMA模式於臺灣月流量資料之分析上具有較佳之適用性。 In the past, difference and detrended methods were usually used in analyzing long-memory hydrological time series. Recently, a k-factor GARMA model was proposed to model long-memory time series, and its forecasting results are better than conventional methods. The major purpose of this study is to examine the suitability of this model, and then apply it to monthly riverflow data of Taiwan. In this study, approximate maximum likelihood method proposed by Hosking(1984) is used to estimate the parameters of k-factor GARMA model, and AIC and BIC are used for model identification. Besides, MSE﹑MAPE and UI are used as criteria for comparison of forecasting. The accuracy of approximate maximum likelihood method is affected by sample size. The larger the sample size, the better parameter estimation accuracy. The results of model identification are affected by parameter and sample size. The BIC criterion has better results in model identification than AIC criterion. On the other hand, the performance of k-factor GARMA model is better than detrended model in preserving skewness when real data are analyzed. To the opposite, detrended model fits better to the mean and variance than k-factor GARMA model. The forecasting results show that k-factor GARMA model is better than detrended model, especially the low streamflow . In conclusion, k-factor GARMA model has better forecasting ability than detrended model, and improves preserving skewness. In general, the k-factor GARMA model is a reasonable model for the monthly riverflow forecasting of Taiwan.
Relation:	農業工程學報 46(4)，頁 20-32
Appears in Collections:	[Graduate Institute & Department of Water Resources and Environmental Engineering] Journal Article

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