Question
a. Get a time series plot, SACF, and SPACF for the data. Do the plots indicate that the series is stationaryandnon-seasonal? Explain. b. Get the
a. Get a time series plot, SACF, and SPACF for the data. Do the plots indicate that the series is stationaryandnon-seasonal? Explain.
b. Get the 1stdifference (d1) of the series. Dothe time series, SACF, and SPACF plots for d1 indicate that the series is stationary?Explain.
c. What type of tentative ARMA model would you choose for the transformed data based on SACF and SPACF of the transformed series? Andwhy?
d.Use MA(1) model as the tentative model to fit the transformed data.Write down the model with assumptions and algebraically expand this model and express Yt as a function of past time series values, constant, and error terms.
e.Test the significant of constant and make the decision about whether to include the constant term. Estimate the model parameter(s).
f. Find forecast value for period 111 to 113 manually and compare your answers with SPSS output. If you are given the observationY111=6.0051 Update your forecast for period 112 to 113.
g. Use AR(1) model as the tentative model to fit the transformed data. Estimate the model parameter(s). Find forecast value for period 111 to 113. If you are given the observationY111=6.0051. Update your forecast for period 112.
data:
| 3.7136 | 1 |
| 3.6636 | 2 |
| 3.912 | 3 |
| 3.6889 | 4 |
| 3.7612 | 5 |
| 3.6376 | 6 |
| 3.7842 | 7 |
| 3.5553 | 8 |
| 3.6636 | 9 |
| 3.5553 | 10 |
| 3.3673 | 11 |
| 3.8918 | 12 |
| 3.912 | 13 |
| 4.0775 | 14 |
| 4.1431 | 15 |
| 3.4657 | 16 |
| 3.6636 | 17 |
| 3.8501 | 18 |
| 3.9703 | 19 |
| 4.0943 | 20 |
| 4.0431 | 21 |
| 3.9512 | 22 |
| 4.2485 | 23 |
| 4.4998 | 24 |
| 4.3041 | 25 |
| 4.1271 | 26 |
| 4.0073 | 27 |
| 4.4308 | 28 |
| 4.5433 | 29 |
| 4.2485 | 30 |
| 4.6821 | 31 |
| 4.9345 | 32 |
| 4.7875 | 33 |
| 4.5747 | 34 |
| 4.8363 | 35 |
| 5.0039 | 36 |
| 5.0626 | 37 |
| 4.8203 | 38 |
| 4.9416 | 39 |
| 4.6913 | 40 |
| 4.7362 | 41 |
| 4.3438 | 42 |
| 4.7875 | 43 |
| 4.8903 | 44 |
| 4.7005 | 45 |
| 4.5218 | 46 |
| 4.5747 | 47 |
| 4.3567 | 48 |
| 4.5951 | 49 |
| 4.6728 | 50 |
| 4.7185 | 51 |
| 4.4998 | 52 |
| 4.585 | 53 |
| 4.8283 | 54 |
| 5.0434 | 55 |
| 5.247 | 56 |
| 5.4638 | 57 |
| 5.2417 | 58 |
| 5.1591 | 59 |
| 5.1818 | 60 |
| 4.9127 | 61 |
| 5.0814 | 62 |
| 5.1417 | 63 |
| 5.0039 | 64 |
| 5.2149 | 65 |
| 5.0434 | 66 |
| 5.6204 | 67 |
| 5.4116 | 68 |
| 5.3613 | 69 |
| 5.6312 | 70 |
| 5.591 | 71 |
| 5.6595 | 72 |
| 5.4723 | 73 |
| 5.3613 | 74 |
| 5.5491 | 75 |
| 5.6802 | 76 |
| 5.3566 | 77 |
| 5.5053 | 78 |
| 5.8665 | 79 |
| 5.826 | 80 |
| 5.7301 | 81 |
| 5.5094 | 82 |
| 5.5491 | 83 |
| 5.7746 | 84 |
| 5.6971 | 85 |
| 5.6095 | 86 |
| 5.743 | 87 |
| 5.5175 | 88 |
| 5.656 | 89 |
| 5.6312 | 90 |
| 5.7333 | 91 |
| 5.994 | 92 |
| 5.7333 | 93 |
| 5.793 | 94 |
| 5.8665 | 95 |
| 5.8693 | 96 |
| 5.79 | 97 |
| 5.7807 | 98 |
| 5.6525 | 99 |
| 5.4931 | 100 |
| 5.4848 | 101 |
| 5.6595 | 102 |
| 5.8721 | 103 |
| 6.1312 | 104 |
| 5.8972 | 105 |
| 6.1883 | 106 |
| 6.1137 | 107 |
| 5.9687 | 108 |
| 6.2146 | 109 |
| 6.1115 | 110 |
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Topology
Authors: Marco Manetti
1st Edition
3319169580, 9783319169583
