(a) Suppose that from a time series of 100 observations. .51 : 0.49. r; : 0.31. :3 : 0.2]. n; = 0.11. and |r.5.| 0.09 for It 4. On this basis alone, which ARIMA model would be tentatively chosen for the series? (3 marks) (b) Suppose that from a stationary time series of length 121 the sample partial autooorrelations are (.5 3 :0. 8 .5533 _ 0. 6. (.53 33 :0. 08 and 35544 _ 0. 0. Based on this information alone which ARIMA model would be tentatively chosen for the series? (3 marks) (c) For a time series of 169 observations we nd that 51 _ 0.41. 52 _ 0.3 2.53 _ 0. 26 54 _ 0.21. and 55 _ 0.16. Which ARIMA model ts this pattern of autocorrelations'? (4 marks) (d) If {2}} satisfies an ARM) model with (.5 of about 0.7, how long should the series be if we need to estimate (.5 : ll with 95% condence that our estimation error is no more than :0]