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Unformatted text preview: Time Series (MA3/50085) 2005 Exercises 4 1. Find the partial ACF of the AR(2) process given by X t = 1 3 X t 1 + 29 X t 2 + t . 2. Suppose that a correlogram of a time series consisting of 100 observations has r 1 = 0 . 31 ,r 2 = 0 . 37 ,r 3 = . 05 ,r 4 = 0 . 06 ,r 5 = . 21 ,r 6 = 0 . 11 ,r 7 = . 08 ,r 9 = 0 . 12 ,r 10 = . 01. Suggest an ARMA model which may be appropriate. 3. The first eight values of the ACF and PACF of 60 observations on a quarterly economic index, and of the first differences are shown below Lag 1 2 3 4 5 6 7 8 X t ,r k 0.95 0.91 0.87 0.82 0.79 0.74 0.70 0.67 X t , kk 0.95 0.040.05 0.07 0.00 0.070.040.02 X t ,r k 0.02 0.08 0.12 0.050.020.050.01 0.03 X t , k,k 0.02 0.08 0.06 0.030.050.060.040.02 Identify a model for the series. 4. The local level model consists of two equations Y t = t + t (1) t = t 1 + h t (2) where h t is white noise with variance 2 h , and is uncorrelated with t ....
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 Spring '09
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