T8 - STA4005B Time Series (2007-2008) Tutorial 8 (18/3,...

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Unformatted text preview: STA4005B Time Series (2007-2008) Tutorial 8 (18/3, 19/3) (Time & Venue: T9, BMS LT; W5, MMW 704) Estimation Methods Suppose a sample realization { is obtained and ARIMA model is proposed to fit the data. } n t Z t , , 2 , 1 , K = Then we want to estimate the parameters in the model after model specification. For an ARIMA model , ) ( ) ( ) 1 )( ( t t d a B Z B B θ µ φ = − − we want to estimate the parameters , µ , ' s φ s ' θ and . 2 a σ 1. Method of Moment First find some formulas are related to the population moment and the parameters which you want to estimate. Then replace the population moment by sample moment and solve for the parameters. Population Moment Sample Moment µ ∑ = = n t t Z n Z 1 1 j ρ j r γ 2 1 2 ) ( 1 1 Z Z n S n t t − − = ∑ = or 2 1 ) ( 1 Z Z n c n t t − = ∑ = For example, a) For time series with mean µ , the estimator of mean is the sample mean Z ....
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This note was uploaded on 11/02/2011 for the course STAT 4005 taught by Professor Wu,kaho during the Spring '08 term at CUHK.

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T8 - STA4005B Time Series (2007-2008) Tutorial 8 (18/3,...

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