利用類經驗模分解於時間序列ARMA模型係數估計之探討

The Application of Empirical Mode Decomposition on Parameter Estimation of ARMA Model in Time Series

張佑瑋(Yu-Wei Chang)

指導教授 ： 林財川

國立臺北大學/商學院/統計學系/碩士(2010年)

摘要

利用類經驗模分解(empirical mode decomposition；EMD)及自我共變異函數(autocovariance function；ACF)的減幅正弦曲線模型(damped sinusoid model；DSM)來估計AR模型係數方程式的根，有別於傳統直接估計係數的方法。本研究基於希爾伯特-黃轉換(Hilbert-Huang transform)可處理非穩定及非線性之特性，先將時間序列之自我共變異函數以經驗模態分解處理而得到內部模態函數(intrinsic mode function；IMF)，再將內部模態函數配適減幅正弦曲線模型，估計出AR模型係數方程式的根。此方法可推廣到ARMA模型當中，先以同樣的方法來估計ARMA模型當中AR係數方程式的根,再佐以傳統估計係數方法處理MA模型係數估計。此方法可以直接找出最佳的分解，以減少計算的繁複程度。

關鍵詞：自我共變異函數、減幅正弦曲線模型、希爾伯特-黃轉換、經驗模態分解、內部模態函數。

關鍵字

自我共變異函數 ； 減幅正弦曲線模型 ； 希爾伯特-黃轉換 ； 經驗模態分解 ； 內部模態函數

並列摘要

The parameter estimation using the empirical mode decomposition and damped sinusoid model to estimate the roots of autoregressive equation is different from the traditional methods that estimate parameter directly. This search is based on the property of Hilbert-Huang transform that can deal with nonstationary or nonlinear time series data. First, we use empirical mode decomposition to decompose autocovarinace function of time series into intrinsic mode functions. Consequently, we fit a damped sinusoid model to these intrinsic mode functions to estimate the roots of AR model. This method can also be applied to the ARMA model. Basically, one can carry out the roots of parameter function of AR system for an ARMA model in the same way and use traditional method to estimate the parameter of MA system for an ARMA model.

Keyworlds: damped sinusoid model, Hilbert-Huang transform, empirical mode decomposition, intrinsic mode functio

並列關鍵字

damped sinusoid model ； Hilbert-Huang transform ； empirical mode decomposition ； intrinsic mode functio

參考文獻

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