Question One [10 marks] A time series of n = 100 observations gave the following sample ACF and sample PACF, Lag k 1 2 3 4 5 6 7 8 TK 0.22 -0.68 -0.47 -0.34 0.56 -0.01 -0.51 0.26 Pkk 0.22 -0.76 -0.09 0.05 0.09 0.04 -0.11 -0.11 with the sample mean Z = 10.04 and sample variance Vo = 2.77. An AR(2) model, (1 - 41B - 42B2)Zt = 8 + at, appears to be appropriate for the data. a) Obtain the Yule-Walker estimates @1 and $2. b) Using $1 and $2 as the true values of 41 and 42, calculate PK, k = 1,2,3. c) . Consider the following set of data: {23.32,32.33,32.88,28.98,33.16,26.33,29.88,32.69,18.98,21.23,26.66,29.89} Calculate the lag-one sample autocorrelation of the time series