chap5 - ARMA Modeling and Forecasting(Chap 5 5.1...

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1 1 ARMA Modeling and Forecasting (Chap 5) 5.1 Preliminary Estimation Useful for order identification (requires the fitting of a number of competing models). initial parameter estimates for likelihood optimization. ARMA(p,q) Model: Based on observations x 1 ,..., x n , from the model φ( B) X t = θ( B) Z t , { Z t } ~ WN(0, σ 2 ), want to estimate φ = φ =(φ 1 , . . ., φ p ) and θ = θ =(θ 1 , . . ., θ p ) , where the orders p and q are assumed known (for the moment). 2 AR(p) Processes: Yule-Walker Estimation (moment estimates) Burg Estimation ARMA(p,q) Processes: Innovations Algorithm Hannan-Rissanen Estimates
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