Question
Twenty Five successive observations on a stationary time series are given as follows: 30, 33, 32, 27, 25, 28, 29, 31, 35, 34, 38, 31, 23, 24, 34, 36, 29, 32, 38, 27, 22, 29, 20, 40, 37. Calculate r1, r2, ....., r10 and plot the correlogram.
Answer :
Word Count : 824
We first construct the following table:
| Y | Y2 | (Yt-á¿©) | (Yt-á¿©)(Yt+1 - á¿©) | (Yt-á¿©)(Yt+2 - á¿©) | (Yt-á¿©)(Yt+3 - á¿©) | (Yt-á¿©)(Yt+4 - á¿©) | (Yt-á¿©)(Yt+5 - á¿©) | (Yt-á¿©)(Yt+6 - á¿©) | (Yt-á¿©)(Yt+7 - á¿©) | (Yt-á¿©)(Yt+8 - á¿©) | (Yt-á¿©)(Yt+9 - á¿©) | (Yt-á¿©)(Yt+10 - á¿©) | |
| 1 | 30 | 900 | -0.56 | ||||||||||
| 2 | 33 | 1089 | 2.44 | -1.3664 | |||||||||
| 3 | 32 | 1024 | 1.44 | 3.5136 | -0.8064 | ||||||||
| 4 | 27 | 729 | -3.56 | -5.1264 | -8.6864 | 1.9936 | |||||||
| 5 | 25 | 625 | -5.56 | 19.7936 | -8.0064 | -13.5664 | 3.1136 | ||||||
| 6 | 28 | 784 | -2.56 | 14.2336 | 9.1136 | -3.6864 | -6.2464 | 1.4336 | |||||
| 7 | 29 | 841 | -1.56 | 3.9936 | 8.6736 | 5.5536 | -2.2464 | -3.8064 | 0.8736 | ||||
| 8 | 31 | 961 | 0.44 | -0.6864 | -1.1264 | -2.4464 | -1.5664 | 0.6336 | 1.0736 | -0.2464 | |||
| 9 | 35 | 1225 | 4.44 | 1.9536 | -6.9264 | __________ ________ ______ _____ ______ ______ ________ _______.