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# hw3 - 3(1 point each Identify the following model with ACF...

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- The homework has to be stapled. PSTAT 174/274. Homework #3 Name: Due: 10/30/06 at the beginning of the discussion session Score: /10 Credit: People you worked with: Sources consulted(Reference): 1. (1 point each) Suppose that X t is a stationary time series with mean μ and ACF ρ ( · ). (a) Write the best one step ahead predictor, X n +1 of the form aX n + b with μ and ρ ( · ). (b) Write the best m step ahead predictor, X n + m of the form a 0 X n + b 0 with μ and ρ ( · ). 2. Consider the following AR(1) time series model X t = 0 . 6 X t - 1 + w t , w t i.i.d N (0 , 1) (a) (1 point) Find the partial autocorrelation with lag 1, φ 11 . (b) (1 point) Find the partial autocorrelation with lag 2, φ 22 . (c) (R homework - 0.5 point each) You need to provide R-code and Plot for full credit. First, simulate the time series. i. Plot ACF. ii. Plot PACF. (d) (2 points) Determine m step ahead predictor and the corresponding MSE.
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Unformatted text preview: 3. (1 point each) Identify the following model with ACF and PACF. First, you need to read the data from the web by typing > load(url(‘http://www.pstat.ucsb.edu/faculty/choih/PSTAT174/hw3.r’)) Now you have three time series in R - ts1, ts2, ts3. You need to provide the plots for the following questions. (a) Plot ACF and PACF of ts1. Which model would you ﬁt ts1? Explain. a. AR(1) b. MA(1) c. AR(2) d. MA(2) e. ARMA(1,1) (b) Plot ACF and PACF of ts2. Which model would you ﬁt ts2? Explain. a. AR(1) b. MA(1) c. AR(2) d. MA(2) e. ARMA(1,1) (c) Plot ACF and PACF of ts3. Which model would you ﬁt ts3? Explain. a. AR(1) b. MA(1) c. AR(2) d. MA(2) e. ARMA(1,1)...
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