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Unformatted text preview: STA4005B Time Series (2007-2008) Tutorial 9 (25/3, 26/3) (Time & Venue: T9, BMS LT; W5, MMW 704) Estimation Methods 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 Z j ρ j r γ 2 S or c 2. Conditional Least Square Method (a) Autoregressive Process Consider an AR(p) process: t p t p t t a Z Z Z + − + + − = − − − ) ( ) ( 1 1 µ φ µ φ µ L i. Rewrite the above equation so that we can fit a regression model on . t Z ii. Which quantity is minimized in the least square estimation? iii. How to estimate the parameters in the above model? 1 Example 1 Suppose we have a AR(1) model t t t a Z Z + + = − 1 φ θ with ) , ( ~ 2 a t WN a σ Computer ouput (S-plus): Coefficients: Value Std. Error t value Pr(>|t|) (Intercept) 5.6421 0.8921 6.3245 0.0000 Zt.1 0.6250 0.1019 6.1335 0.0000 Residual standard error: 2.862 on 78 degrees of freedom Residual standard error: 2....
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- Spring '08
- Maximum likelihood, Likelihood function, population moment, sample moment