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hw1 - Shumway and Sto²er problem 1.7 4(ACF and forecasting...

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Stat153 Assignment 1 (due September 10, 2010) 1. (White noise) We have seen that i.i.d. noise is white noise. ‘This example shows that white noise is not necessarily i.i.d. Suppose that { W t } and { Z t } are independent and identically distributed (i.i.d.) sequences, with P ( W t = 0) = P ( W t = 1) = 1 / 2 and P ( Z t = - 1) = P ( Z t = 1) = 1 / 2. Defne the time series model X t = W t (1 - W t - 1 ) Z t . Show that { X t } is white but not i.i.d. 2. (Stationarity) For each o± the ±ollowing, state i± it is a stationary process. I± so, give the mean and autocovariance ±unctions. Here, { W t } is i.i.d. N(0,1). (a) X t = W t - W t - 3 . (b) X t = W 3 . (c) X t = t + W 3 . (d) X t = W 2 t . (e) X t = W t W t - 2 . 3. (MA process and ACF)
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Unformatted text preview: Shumway and Sto²er problem 1.7. 4. (ACF and forecasting) Shumway and Sto²er problem 1.10a,b. (Notice that the autocorrelation ±unction is denoted by ρ , not γ .) 5. (Computer exercise: AR processes) Shumway and Sto²er problem 1.3. 6. (Computer exercise: Sample ACFs) Generate n = 100 observations o± the time series ±rom Shumway and Sto²er problem 1.7: X t = W t-1 + 2 W t + W t +1 , where { W t } ∼ WN (0 , 1). Compute and plot the sample autocorrelation ±unction. 1...
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