本篇文章之主要目的是將Efron於1979年所提出之拔靴法(Bootstrap method)應用在非常態ARMA(p,q)模式上。我們考慮的結構包括AR(1)，AR(2)，MA(1)，MA(2)，ARMA(1,1)，而考慮的非常態干擾分配則包括對數常態分配，均勻分配，迦瑪分配以及指數分配，對每一個模式，所設定之參數值組合涵蓋了使模式平穩及/或可逆之參數組合中的重要區域。我們比較傳統的最小平方法與利用500個拔靴重複子(Bootstrap repetitions)的拔靴法在參數估計上的差異。進一步我們也以MAE及MAPE等準則比較了這兩種估計模式在預測上的優劣。模擬結果顯示，在參數估計方面，當所設定的參數範圍接近非平穩或非可逆條件時，拔靴法所獲得的參數估計值表現會較佳。然而在預測效益方面，利用往前一期預測法，並配合拔靴法重新改造的數列，在具有非常態干擾項AR(1)，AR(2)以及ARMA(1,1)模式的預測效益上的確有較佳的效果。
關鍵詞：拔靴法，非常態ARMA(p,q) ，最小平方法 / In this thesis, the Bootstrap technique proposed by Efron in 1979 is applied to parameter estimation and forecasting of non-normal ARMA(p,q) time series models. A simulation study is conducted where artificial time series are generated from various ARMA structures with different non-normal noise distributions. The ARMA structures considered in the simulation are AR(1), AR(2), MA(1), MA(2) and ARMA(1,1), while the non-normal noise distributions include Log-normal, Uniform, Gamma, and Exponential distributions. For each structure, the parameter values used cover important regions of the stationary and/or invertible parameter space . The conventional least-square estimators of the parameters are compared with the corresponding non-parametric Bootstrap estimator, obtained by using 500 Bootstrap repetitions for each series. Furthermore, forecasts based on these estimated model are also compared by using such criteria as MAE and MAPE .
KEY WORDS bootstrap; non-normal ARMA(p,q); least-square
| Identifer | oai:union.ndltd.org:CHENGCHI/B2002001567 |
| Creators | 郭玉麟 |
| 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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