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时间序列分析课后习题答案1

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时间序列分析课后习题答案(上机)

第二章 2、

3423403383363343323303281975197619771978X19791980

(1)时序图如上:序列具有明显的趋势和周期性,该序列非平稳。 (2)样本自相关系数:

(3)该样本自相关图上,自相关系数衰减为0的速度缓慢,且有正弦波状,显示序列具有趋势和周期,非平稳。 3、(1)样本自相关系数:

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(2)序列平稳。

(3)因Q统计量对应的概率均大于0.05,故接受该序列为白噪声的假设,即序列为村随机序列。

5、(1)时序图和样本自相关图:

3503002502001501005000:0100:0701:0101:0702:0102:0703:0103:07X

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(2)序列具有明显的周期性,非平稳。

(3)序列的Q统计量对应的概率均小于0.05,该序列是非白噪声的。 6、(1)

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根据样本相关图可知:该序列是非平稳,非白噪声的。 (2)对该序列进行差分运算:ytxtxt1 {yt}的样本相关图:

该序列平稳,非白噪声。

第三章:17、(1)

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结论:序列平稳,非白噪声。

(2)拟合MA(2) model:

Variable

C MA(1) MA(2) R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Inverted MA Roots

Coefficient 80.40568 0.336783 0.343877 Std. Error 4.630308 0.114610 0.116874 t-Statistic 17.36508 2.938519 2.942297 Prob. 0.0000 0.0047 0.0046 0.171979 Mean dependent var 80.29524 0.144379 S.D. dependent var 21.94078 Akaike info criterion 28883.87 Schwarz criterion -282.4221 F-statistic 2.0720 Prob(F-statistic) -.17+.56i -.17 -.56i

23.71981 9.061019 9.163073 6.230976 0.003477

Residual tests

(3)拟合AR(2)model:

Variable C AR(1)

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Coefficient 79.71956 0.258624

Std. Error 5.442613 0.128810

t-Statistic 14.729 2.007794

Prob. 0.0000 0.0493

AR(2) R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Inverted AR Roots

0.227469 0.125114 1.818102 0.0742 23.35053 9.052918 9.156731 5.306195 0.007651

0.1672 Mean dependent var 79.50492 0.125522 S.D. dependent var 21.83590 Akaike info criterion 276.79 Schwarz criterion -273.1140 F-statistic 1.939572 Prob(F-statistic) .62 -.36

Residual tests:

(4) 拟合ARMA(2,1)model:

Variable C AR(1) AR(2) MA(1) R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood

Coefficient 79.17503 -0.586834 0.376120 1.113999 Std. Error 4.082908 0.118000 0.082091 0.097122 t-Statistic 19.39183 -4.973170 4.581756 11.47012 Prob. 0.0000 0.0000 0.0000 0.0000 23.35053 8.840611 8.979029 9.719104

0.338419 Mean dependent var 79.50492 0.303599 S.D. dependent var 19.48617 Akaike info criterion 213.51 Schwarz criterion -265.6386 F-statistic

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Durbin-Watson stat Inverted AR Roots Inverted MA Roots

1.963688 Prob(F-statistic) .39 -.97 -1.11

Estimated MA process is noninvertible

0.000028 残差检验:

(5)拟合ARMA(1,(2))model:

Variable C AR(1) MA(2) R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Inverted AR Roots

Coefficient 79.52100 0.270506 0.233914 Std. Error 4.621910 0.125606 0.130773 t-Statistic 17.20523 2.153603 1.788701 Prob. 0.0000 0.03 0.0788 0.157273 Mean dependent var 79.55161 0.128706 S.D. dependent var 21.61946 Akaike info criterion 27576.65 Schwarz criterion -276.9995 F-statistic 1.981887 Prob(F-statistic) .27

23.16126 9.032242 9.135167 5.505386 0.0023 残差检验:

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(6)优化 model MA(2) AR(2) ARMA(2,1) ARMA(1,(2)) AIC 9.0610 9.0529 8.8406 9.0322 SC 9.1631 9.1567 8.9790 9.1352 根据SC准则,最优模型为ARMA(2,1)模型。

(7)预测: 年份 19 1965 1966 1967 1968 预测值 83.80630 88.05114 75.70815 84.800 74.71802 标准差 19.48617 22.02801 22.06639 22.28311 22.32277 95%的置信下限 95%的置信上限 45.61341 44.87624 32.45803 40.87310 30.96539 121.9992 131.226 118.9583 128.2229 118.4706 word文档 可自由复制编辑

18、(1)平稳性判断与纯随机性检验:

序列平稳,非白噪声。

(2)拟合AR(1)model:

Variable C AR(1)

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Inverted AR Roots Coefficient 0.8441 0.3725

Std. Error 0.052013 0.111569

t-Statistic 16.227 3.339322

Prob. 0.0000 0.0013

0.135739 Mean dependent var 0.8495 0.123566 S.D. dependent var 0.278633 Akaike info criterion 5.512162 Schwarz criterion -9.284669 F-statistic 2.068675 Prob(F-statistic) .37 0.297627 0.309169 0.371921 11.15107 0.001341 残差检验:

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(3)拟合MA(6)model:

Variable C MA(1) MA(2) MA(4) MA(6) R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Inverted MA Roots

Coefficient 0.837270 0.201853 0.301118 0.278566 0.270084 Std. Error 0.0651 0.1102 0.104814 0.110528 0.115984 t-Statistic 12.75526 1.830225 2.872875 2.520322 2.328636 Prob. 0.0000 0.0715 0.00 0.0140 0.0228 0.851216 0.295913 0.313720 0.469400 4.037420 0.005328 0.1662 Mean dependent var 0.142686 S.D. dependent var 0.2739 Akaike info criterion 5.179833 Schwarz criterion -6.607637 F-statistic 1.867536 Prob(F-statistic) -.68+.53i -.68 -.53i .61+.50i .61 -.50i -.04 -.77i -.04+.77i

残差检验:

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(4)拟合ARMA((2),1)model

Variable C AR(2) MA(1) R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Inverted AR Roots Inverted MA Roots Coefficient 0.852299 0.260738 0.452777 Std. Error 0.061255 0.123711 0.117596 t-Statistic 13.91390 2.1070 3.850279 Prob. 0.0000 0.0387 0.0003 0.219781 Mean dependent var 0.855139 0.197166 S.D. dependent var 0.265118 Akaike info criterion 4.849841 Schwarz criterion -5.0456 F-statistic 2.041391 Prob(F-statistic) .51 -.51 -.45 0.295887 0.223490 0.318351 9.718346 0.000191 残差检验:

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(5)优化 model AR(1) MA(6) ARMA((2),1) AIC 0.3092 0.3137 0.2235 SC 0.3719 0.4694 0.3184 根据SC准则,最优模型为ARMA((2),1)模型。

(6)预测: 年份 1975 1976 1977 1978 1979 预测值 0.774 0.75001 0.796 0.82563 0.83839 标准差 0.26512 0.29103 0.29912 0.30076 0.30130 95%的置信下限 95%的置信上限 0.12810 0.17960 0.21268 0.23615 0.24785 1.16737 1.32042 1.38524 1.41511 1.423 word文档 可自由复制编辑

18.(1)

序列平稳,非白噪声

(2)拟合AR(3)模型:

Variable C AR(1) AR(2) AR(3) R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Inverted AR Roots

Coefficient 84.13028 -0.395022 -0.298634 -0.186335 Std. Error 0.100370 0.070460 0.072652 0.070027 t-Statistic 838.2004 -5.606293 -4.110476 -2.660918 Prob. 0.0000 0.0000 0.0001 0.0084 0.1612 Mean dependent var 84.12980 0.148320 S.D. dependent var 2.655132 Akaike info criterion 1367.7 Schwarz criterion -472.2752 F-statistic 2.001728 Prob(F-statistic) .06 -.60i .06+.60i -.52

2.877053 4.810861 4.877291 12.43581 0.000000 word文档 可自由复制编辑

残差检验:

(3)拟合AR(1,2,3,6)模型:

Variable C AR(1) AR(2) AR(3) AR(6) R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Inverted AR Roots

Coefficient 84.14284 -0.395527 -0.304273 -0.1818 0.148199 Std. Error 0.1087 0.0707 0.073440 0.070624 0.065240 t-Statistic 773.4515 -5.590134 -4.143128 -2.575110 2.271609 Prob. 0.0000 0.0000 0.0001 0.0108 0.0242 0.186539 Mean dependent var 84.13128 0.169414 S.D. dependent var 2.633285 Akaike info criterion 1317.496 Schwarz criterion -462.9657 F-statistic 1.92 Prob(F-statistic) 2.8386 4.7998 4.883571 10.251 0.000000 -.i

-.37+.i -.79

.59 .27 -.71i .27+.71i -.37

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残差检验:

(4)拟合MA(1)模型:

Variable C MA(1) R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Inverted MA Roots

Coefficient 84.13042 -0.480740 Std. Error 0.099045 0.062375 t-Statistic 849.4201 -7.707312 Prob. 0.0000 0.0000 0.148110 Mean dependent var 84.11940 0.143830 S.D. dependent var 2.85 Akaike info criterion 1439.433 Schwarz criterion -483.0610 F-statistic 1.8721 Prob(F-statistic) .48

2.906625 4.8277 4.859346 34.59833 0.000000 残差检验:

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(5)拟合ARMA((1),(1,6))模型:

Variable C AR(2) MA(1) MA(6) R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Inverted MA Roots

Coefficient 84.11553 -0.167970 -0.375134 0.168123 Std. Error 0.126943 0.074565 0.068739 0.065812 t-Statistic 662.6253 -2.252656 -5.457376 2.5578 Prob. 0.0000 0.02 0.0000 0.0114 0.175501 Mean dependent var 84.10402 0.162816 S.D. dependent var 2.6779 Akaike info criterion 1366.061 Schwarz criterion -474.0437 F-statistic 2.001830 Prob(F-statistic) 2.2726 4.804460 4.870657 13.83572 0.000000 -.73i

-.59 -.37i -.59+.37i

.72 -.36i .72+.36i .06+.73i .06

残差检验:

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(6)拟合ARMA(3,(6))模型:

Variable C AR(1) AR(2) AR(3) MA(6) R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Inverted AR Roots Inverted MA Roots

Coefficient 84.12708 -0.388317 -0.320461 -0.1837 0.227526 Std. Error 0.119520 0.070662 0.072472 0.070018 0.071453 t-Statistic 703.8762 -5.4930 -4.421874 -2.624394 3.1842 Prob. 0.0000 0.0000 0.0000 0.0094 0.0017 0.1999 Mean dependent var 84.12980 0.179846 S.D. dependent var 2.605527 Akaike info criterion 1310.232 Schwarz criterion -468.0294 F-statistic 1.990809 Prob(F-statistic) .05+.61i .05 -.61i -.49 .68+.39i .68 -.39i .00 -.78i

-.00+.78i

-.68+.39i -.68 -.39i 2.877053 4.778075 4.861112 11.79970 0.000000 word文档 可自由复制编辑

残差检验:

(7)优化 model AR(3) AR(6) MA(1) ARMA(2,6) ARMA(3,6) AIC 4.8109 4.7996 4.8265 4.8045 4.7781 SC 4.8773 4.8836 4.8593 4.8707 4.8611 根据SC准则,最优模型为MA(1)模型。

(8)预测: 202 预测值 85.69222 标准差 2.85 95%的置信下限 95%的置信上限 80.42083 90.96361 word文档 可自由复制编辑

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