1
4 μ=0, σ=1 5 μ=2, σ=1 5 μ=0, σ=2 3 2 1 0-1 -2-3 0 10 20 30 40 50 60 70 80 90 4 3 2 1 0-1 0 10 20 30 40 50 60 70 80 90 4 3 2 1 0-1 -2-3 -4-5 0 10 20 30 40 50 60 70 80 90 8 μ=2, σ=2 5 μ=1, θ 1 =0.5, σ=1 5 μ=1, θ 1 =0.5, σ=1 6 4 4 4 2 3 2 1 3 2 1 0 0 0-2 -1-1 -4 0 10 20 30 40 50 60 70 80 90-2 0 10 20 30 40 50 60 70 80 90-2 0 10 20 30 40 50 60 70 80 90 2
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3 μ=0, σ=1 5 μ=2, σ=1 6 μ=0, σ=2 2 4 5 4 1 3 3 2 0 2 1-1 1 0-1 -2-3 0 10 20 30 40 50 60 70 80 90 0-1 0 10 20 30 40 50 60 70 80 90-2 -3-4 0 10 20 30 40 50 60 70 80 90 10 μ=2, σ=2 5 μ=1, θ 1 =0.5, σ=1 5 μ=1, θ 1 =0.5, σ=1 8 4 4 6 4 2 0 3 2 1 0 3 2 1 0-1 -2-1 -2-4 0 10 20 30 40 50 60 70 80 90-2 0 10 20 30 40 50 60 70 80 90-3 0 10 20 30 40 50 60 70 80 90 10
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自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 θ 1 =0.5, θ 2 =0 1 2 3 4 5 6 7 8 9 10 ラグ 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 θ 1 =-0.5, θ 2 =0 1 2 3 4 5 6 7 8 9 10 ラグ 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 θ 1 =0.8, θ 2 =0.3 1 2 3 4 5 6 7 8 9 10 ラグ 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 θ 1 =0.3, θ 2 =0.8 1 2 3 4 5 6 7 8 9 10 ラグ 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 θ 1 =0.8, θ 2 =-0.3 1 2 3 4 5 6 7 8 9 10 ラグ 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 θ 1 =-0.8, θ 2 =-0.3 1 2 3 4 5 6 7 8 9 10 ラグ 13
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自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 θ 1 =0.5, θ 2 =0 1 2 3 4 5 6 7 8 9 10 ラグ 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 θ 1 =-0.5, θ 2 =0 1 2 3 4 5 6 7 8 9 10 ラグ 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 θ 1 =0.8, θ 2 =0.3 1 2 3 4 5 6 7 8 9 10 ラグ 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 θ 1 =0.3, θ 2 =0.8 1 2 3 4 5 6 7 8 9 10 ラグ 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 θ 1 =0.8, θ 2 =-0.3 1 2 3 4 5 6 7 8 9 10 ラグ 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 θ 1 =-0.8, θ 2 =-0.3 1 2 3 4 5 6 7 8 9 10 ラグ 17
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5 c=1, φ 1 =0.5, σ=1 120 c=1, φ 1 =1, σ=1 120000 c=1, φ 1 =1.1, σ=1 4 100 100000 3 80 80000 2 1 0 60 40 60000 40000-1 20 20000-2 0 10 20 30 40 50 60 70 80 90 0 0 10 20 30 40 50 60 70 80 90 0 0 10 20 30 40 50 60 70 80 90 0 c=-2, φ 1 =0.3, σ=0.5 4 c=0, φ 1 =-0.3, σ=2 3 c=-2, φ 1 =-0.8, σ=1-0.5-1 -1.5-2 -2.5-3 -3.5-4 3 2 1 0-1 -2-3 -4-5 2 1 0-1 -2-3 -4-4.5 0 10 20 30 40 50 60 70 80 90-6 0 10 20 30 40 50 60 70 80 90-5 0 10 20 30 40 50 60 70 80 90 21
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自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 φ 1 =0.8, φ 2 =0 1 5 10 15 20 ラグ φ 1 =0.1, φ 2 =0.5 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 φ 1 =-0.8, φ 2 =0 1 5 10 15 20 ラグ φ 1 =0.5, φ 2 =-0.8 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 φ 1 =0.5, φ 2 =0.35 1 5 10 15 20 ラグ φ 1 =0.9, φ 2 =-0.8 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 1 5 10 15 20 ラグ 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 1 5 10 15 20 ラグ 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 1 5 10 15 20 ラグ 24
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自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 φ 1 =0.8, φ 2 =0 1 5 10 15 20 ラグ φ 1 =0.1, φ 2 =0.5 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 φ 1 =-0.8, φ 2 =0 1 5 10 15 20 ラグ φ 1 =0.5, φ 2 =-0.8 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 φ 1 =0.5, φ 2 =0.35 1 5 10 15 20 ラグ φ 1 =0.9, φ 2 =-0.8 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 1 5 10 15 20 ラグ 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 1 5 10 15 20 ラグ 自己相関 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-0.1 0-0.2-0.3-0.4-0.5-0.6-0.7-0.8 1 5 10 15 20 ラグ 28
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Correlogram of DATA1 Autocorrelation Partial Correlation AC PAC Q-Stat Prob 1 0.859 0.859 186.50 0.000 2 0.649-0.333 293.64 0.000 3 0.464 0.029 348.57 0.000 4 0.314-0.038 373.78 0.000 5 0.201 0.003 384.20 0.000 6 0.110-0.058 387.30 0.000 7 0.013-0.116 387.34 0.000 8-0.080-0.057 389.02 0.000 9-0.134 0.059 393.71 0.000 10-0.170-0.086 401.29 0.000 11-0.182 0.032 410.00 0.000 12-0.147 0.111 415.71 0.000 13-0.109-0.063 418.89 0.000 14-0.095-0.059 421.27 0.000 15-0.081 0.027 423.03 0.000 16-0.031 0.147 423.29 0.000 17 0.046 0.074 423.85 0.000 18 0.133 0.048 428.63 0.000 19 0.188-0.051 438.28 0.000 20 0.182-0.078 447.31 0.000 49
Correlogram of DATA2 Autocorrelation Partial Correlation AC PAC Q-Stat Prob 1 0.423 0.423 45.187 0.000 2 0.279 0.122 64.895 0.000 3-0.108-0.325 67.889 0.000 4 0.013 0.176 67.934 0.000 5 0.012 0.091 67.972 0.000 6-0.054-0.264 68.738 0.000 7-0.065 0.060 69.836 0.000 8-0.042 0.132 70.298 0.000 9 0.048-0.061 70.894 0.000 10 0.102 0.077 73.636 0.000 11 0.166 0.192 80.884 0.000 12 0.069-0.168 82.135 0.000 13 0.052 0.005 82.860 0.000 14 0.002 0.159 82.862 0.000 15 0.129 0.064 87.314 0.000 16 0.096-0.071 89.785 0.000 17-0.006-0.074 89.795 0.000 18-0.165-0.101 97.160 0.000 19-0.145 0.014 102.88 0.000 20-0.044 0.053 103.41 0.000 50
Correlogram of DATA3 Autocorrelation Partial Correlation AC PAC Q-Stat Prob 1 0.662 0.662 111.00 0.000 2 0.309-0.232 135.19 0.000 3 0.247 0.280 150.74 0.000 4 0.214-0.096 162.48 0.000 5 0.145 0.054 167.88 0.000 6 0.102-0.013 170.55 0.000 7 0.126 0.104 174.67 0.000 8 0.085-0.126 176.52 0.000 9-0.048-0.101 177.13 0.000 10-0.129-0.062 181.48 0.000 11-0.079 0.083 183.10 0.000 12-0.015 0.005 183.16 0.000 13-0.043-0.046 183.65 0.000 14-0.068 0.003 184.89 0.000 15-0.022 0.052 185.02 0.000 16 0.001-0.009 185.02 0.000 17-0.024 0.009 185.18 0.000 18 0.002 0.049 185.18 0.000 19 0.046-0.025 185.75 0.000 20 0.022-0.044 185.89 0.000 51
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Correlogram of DATA3 Autocorrelation Partial Correlation AC PAC Q-Stat Prob 1 0.662 0.662 111.00 0.000 2 0.309-0.232 135.19 0.000 3 0.247 0.280 150.74 0.000 4 0.214-0.096 162.48 0.000 5 0.145 0.054 167.88 0.000 6 0.102-0.013 170.55 0.000 7 0.126 0.104 174.67 0.000 8 0.085-0.126 176.52 0.000 9-0.048-0.101 177.13 0.000 10-0.129-0.062 181.48 0.000 11-0.079 0.083 183.10 0.000 12-0.015 0.005 183.16 0.000 13-0.043-0.046 183.65 0.000 14-0.068 0.003 184.89 0.000 15-0.022 0.052 185.02 0.000 16 0.001-0.009 185.02 0.000 17-0.024 0.009 185.18 0.000 18 0.002 0.049 185.18 0.000 19 0.046-0.025 185.75 0.000 20 0.022-0.044 185.89 0.000 58
Correlogram of Residuals from ARMA(1,2) model Autocorrelation Partial Correlation AC PAC Q-Stat Prob 1 0.001 0.001 0.0003 2-0.011-0.011 0.0304 3 0.006 0.007 0.0411 4 0.079 0.079 1.6273 0.202 5 0.009 0.009 1.6487 0.439 6-0.037-0.036 2.0008 0.572 7 0.088 0.088 4.0221 0.403 8 0.090 0.084 6.1219 0.295 9-0.038-0.039 6.5008 0.369 10-0.132-0.129 11.031 0.137 11-0.004-0.018 11.035 0.200 12 0.062 0.048 12.045 0.211 13-0.004 0.009 12.048 0.282 14-0.095-0.081 14.425 0.210 15 0.017 0.001 14.501 0.270 16 0.033 0.021 14.787 0.321 17-0.038-0.009 15.185 0.366 18-0.017 0.019 15.262 0.433 19 0.058 0.042 16.164 0.442 20 0.055 0.023 17.001 0.454 59
Correlogram of Residuals from ARMA(1,1) model Autocorrelation Partial Correlation AC PAC Q-Stat Prob 1-0.023-0.023 0.1290 2 0.016 0.015 0.1933 3 0.099 0.099 2.6691 0.102 4 0.101 0.107 5.2902 0.071 5 0.050 0.054 5.9369 0.115 6-0.034-0.044 6.2283 0.183 7 0.095 0.071 8.5380 0.129 8 0.087 0.075 10.507 0.105 9-0.030-0.030 10.744 0.150 10-0.125-0.147 14.849 0.062 11 0.004-0.036 14.853 0.095 12 0.056 0.044 15.691 0.109 13-0.003 0.035 15.694 0.153 14-0.097-0.074 18.212 0.109 15 0.024 0.005 18.369 0.144 16 0.030 0.020 18.617 0.180 17-0.037 0.006 18.981 0.215 18-0.025 0.009 19.148 0.261 19 0.052 0.039 19.877 0.281 20 0.053 0.023 20.630 0.298 60
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