Return to search

時間數列模式之拔靴模擬法研究

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

Identiferoai:union.ndltd.org:CHENGCHI/B2002001567
Creators郭玉麟
Publisher國立政治大學
Source SetsNational Chengchi University Libraries
Language中文
Detected LanguageEnglish
Typetext
RightsCopyright © nccu library on behalf of the copyright holders

Page generated in 0.0016 seconds