Given the time series 53, 43, 66, 48, 52, 42, 44, 56, 44, 58, 41, 54, 51, 56, 38
ID: 3182725 • Letter: G
Question
Given the time series 53, 43, 66, 48, 52, 42, 44, 56, 44, 58, 41, 54, 51, 56, 38, 56, 49, 52, 32, 52, 59, 34, 57, 39, 60, 40, 52, 44, 65, 43: (a) Plot the series. (b) Can you guess an approximate value for the first lag autocorrelation coefficient rho1 based on the plot of the series? (c) Plot Z(t) against Z(t+1), and try again to guess the value of rho1. (d) Calculate and plot the sample autocorrelation function, ^rho(k), for k = 0, 1, 2, 3, 4, 5. (e) Calculate and plot the sample partial autocorrelaition function for k = 0, 1, 2, 3, 4, 5.
Explanation / Answer
Results
Time Values(Z(t)) Z(t-1) Mean of Z(t) Z(t)-Mean of Z(t) Z(t)-K1-MZ(t) Z(t)-K2-MZ(t) Z(t)-K3-MZ(t) Z(t)-K4-MZ(t) Z(t)-K5-MZ(t) Z(t)-K6-MZ(t) (Z(t)-Mean of Z(t))* (Z(t)-K1-MZ(t)) (Z(t)-Mean of Z(t))* (Z(t)-K2-MZ(t)) (Z(t)-Mean of Z(t))* (Z(t)-K3-MZ(t)) (Z(t)-Mean of Z(t))* (Z(t)-K4-MZ(t)) (Z(t)-Mean of Z(t))* (Z(t)-K5-MZ(t)) (Z(t)-Mean of Z(t))* (Z(t)-K6-MZ(t)) (Z(t)-Mean of Z(t))^2 (Z(t)-Mean of Z(t))* (Z(t)-K1-MZ(t)) (Z(t)-Mean of Z(t))* (Z(t)-K2-MZ(t)) (Z(t)-Mean of Z(t))* (Z(t)-K3-MZ(t)) (Z(t)-Mean of Z(t))* (Z(t)-K4-MZ(t)) (Z(t)-Mean of Z(t))* (Z(t)-K5-MZ(t)) (Z(t)-Mean of Z(t))* (Z(t)-K6-MZ(t)) 1 53 49.33333333 3.67 0.00 0.00 0.00 0.00 0.00 0.00 0 0 0 0 0 0 13.44 0.00 0.00 0.00 0.00 0.00 0.00 2 43 43 49.33333333 -6.33 3.67 0.00 0.00 0.00 0.00 0.00 -23.22222222 0 0 0 0 0 40.11 -23.22 0.00 0.00 0.00 0.00 0.00 3 66 66 49.33333333 16.67 -6.33 3.67 0.00 0.00 0.00 0.00 -105.5555556 61.11111111 0 0 0 0 277.78 -105.56 61.11 0.00 0.00 0.00 0.00 4 48 48 49.33333333 -1.33 16.67 -6.33 3.67 0.00 0.00 0.00 -22.22222222 8.444444444 -4.888888889 0 0 0 1.78 -22.22 8.44 -4.89 0.00 0.00 0.00 5 52 52 49.33333333 2.67 -1.33 16.67 -6.33 3.67 0.00 0.00 -3.555555556 44.44444444 -16.88888889 9.777777778 0 0 7.11 -3.56 44.44 -16.89 9.78 0.00 0.00 6 42 42 49.33333333 -7.33 2.67 -1.33 16.67 -6.33 3.67 0.00 -19.55555556 9.777777778 -122.2222222 46.44444444 -26.88888889 0 53.78 -19.56 9.78 -122.22 46.44 -26.89 0.00 7 44 44 49.33333333 -5.33 -7.33 2.67 -1.33 16.67 -6.33 3.67 39.11111111 -14.22222222 7.111111111 -88.88888889 33.77777778 -19.55555556 28.44 39.11 -14.22 7.11 -88.89 33.78 -19.56 8 56 56 49.33333333 6.67 -5.33 -7.33 2.67 -1.33 16.67 -6.33 -35.55555556 -48.88888889 17.77777778 -8.888888889 111.1111111 -42.22222222 44.44 -35.56 -48.89 17.78 -8.89 111.11 -42.22 9 44 44 49.33333333 -5.33 6.67 -5.33 -7.33 2.67 -1.33 16.67 -35.55555556 28.44444444 39.11111111 -14.22222222 7.111111111 -88.88888889 28.44 -35.56 28.44 39.11 -14.22 7.11 -88.89 10 58 58 49.33333333 8.67 -5.33 6.67 -5.33 -7.33 2.67 -1.33 -46.22222222 57.77777778 -46.22222222 -63.55555556 23.11111111 -11.55555556 75.11 -46.22 57.78 -46.22 -63.56 23.11 -11.56 11 41 41 49.33333333 -8.33 8.67 -5.33 6.67 -5.33 -7.33 2.67 -72.22222222 44.44444444 -55.55555556 44.44444444 61.11111111 -22.22222222 69.44 -72.22 44.44 -55.56 44.44 61.11 -22.22 12 54 54 49.33333333 4.67 -8.33 8.67 -5.33 6.67 -5.33 -7.33 -38.88888889 40.44444444 -24.88888889 31.11111111 -24.88888889 -34.22222222 21.78 -38.89 40.44 -24.89 31.11 -24.89 -34.22 13 51 51 49.33333333 1.67 4.67 -8.33 8.67 -5.33 6.67 -5.33 7.777777778 -13.88888889 14.44444444 -8.888888889 11.11111111 -8.888888889 2.78 7.78 -13.89 14.44 -8.89 11.11 -8.89 14 56 56 49.33333333 6.67 1.67 4.67 -8.33 8.67 -5.33 6.67 11.11111111 31.11111111 -55.55555556 57.77777778 -35.55555556 44.44444444 44.44 11.11 31.11 -55.56 57.78 -35.56 44.44 15 38 38 49.33333333 -11.33 6.67 1.67 4.67 -8.33 8.67 -5.33 -75.55555556 -18.88888889 -52.88888889 94.44444444 -98.22222222 60.44444444 128.44 -75.56 -18.89 -52.89 94.44 -98.22 60.44 16 56 56 49.33333333 6.67 -11.33 6.67 1.67 4.67 -8.33 8.67 -75.55555556 44.44444444 11.11111111 31.11111111 -55.55555556 57.77777778 44.44 -75.56 44.44 11.11 31.11 -55.56 57.78 17 49 49 49.33333333 -0.33 6.67 -11.33 6.67 1.67 4.67 -8.33 -2.222222222 3.777777778 -2.222222222 -0.555555556 -1.555555556 2.777777778 0.11 -2.22 3.78 -2.22 -0.56 -1.56 2.78 18 52 52 49.33333333 2.67 -0.33 6.67 -11.33 6.67 1.67 4.67 -0.888888889 17.77777778 -30.22222222 17.77777778 4.444444444 12.44444444 7.11 -0.89 17.78 -30.22 17.78 4.44 12.44 19 32 32 49.33333333 -17.33 2.67 -0.33 6.67 -11.33 6.67 1.67 -46.22222222 5.777777778 -115.5555556 196.4444444 -115.5555556 -28.88888889 300.44 -46.22 5.78 -115.56 196.44 -115.56 -28.89 20 52 52 49.33333333 2.67 -17.33 2.67 -0.33 6.67 -11.33 6.67 -46.22222222 7.111111111 -0.888888889 17.77777778 -30.22222222 17.77777778 7.11 -46.22 7.11 -0.89 17.78 -30.22 17.78 21 59 59 49.33333333 9.67 2.67 -17.33 2.67 -0.33 6.67 -11.33 25.77777778 -167.5555556 25.77777778 -3.222222222 64.44444444 -109.5555556 93.44 25.78 -167.56 25.78 -3.22 64.44 -109.56 22 34 34 49.33333333 -15.33 9.67 2.67 -17.33 2.67 -0.33 6.67 -148.2222222 -40.88888889 265.7777778 -40.88888889 5.111111111 -102.2222222 235.11 -148.22 -40.89 265.78 -40.89 5.11 -102.22 23 57 57 49.33333333 7.67 -15.33 9.67 2.67 -17.33 2.67 -0.33 -117.5555556 74.11111111 20.44444444 -132.8888889 20.44444444 -2.555555556 58.78 -117.56 74.11 20.44 -132.89 20.44 -2.56 24 39 39 49.33333333 -10.33 7.67 -15.33 9.67 2.67 -17.33 2.67 -79.22222222 158.4444444 -99.88888889 -27.55555556 179.1111111 -27.55555556 106.78 -79.22 158.44 -99.89 -27.56 179.11 -27.56 25 60 60 49.33333333 10.67 -10.33 7.67 -15.33 9.67 2.67 -17.33 -110.2222222 81.77777778 -163.5555556 103.1111111 28.44444444 -184.8888889 113.78 -110.22 81.78 -163.56 103.11 28.44 -184.89 26 40 40 49.33333333 -9.33 10.67 -10.33 7.67 -15.33 9.67 2.67 -99.55555556 96.44444444 -71.55555556 143.1111111 -90.22222222 -24.88888889 87.11 -99.56 96.44 -71.56 143.11 -90.22 -24.89 27 52 52 49.33333333 2.67 -9.33 10.67 -10.33 7.67 -15.33 9.67 -24.88888889 28.44444444 -27.55555556 20.44444444 -40.88888889 25.77777778 7.11 -24.89 28.44 -27.56 20.44 -40.89 25.78 28 44 44 49.33333333 -5.33 2.67 -9.33 10.67 -10.33 7.67 -15.33 -14.22222222 49.77777778 -56.88888889 55.11111111 -40.88888889 81.77777778 28.44 -14.22 49.78 -56.89 55.11 -40.89 81.78 29 65 65 49.33333333 15.67 -5.33 2.67 -9.33 10.67 -10.33 7.67 -83.55555556 41.77777778 -146.2222222 167.1111111 -161.8888889 120.1111111 245.44 -83.56 41.78 -146.22 167.11 -161.89 120.11 30 43 43 49.33333333 -6.33 15.67 -5.33 2.67 -9.33 10.67 -10.33 -99.22222222 33.77777778 -16.88888889 59.11111111 -67.55555556 65.44444444 40.11 -99.22 33.78 -16.89 59.11 -67.56 65.44Related Questions
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