时间序列分析课后习题答案1.docx
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时间序列分析课后习题答案1.docx
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时间序列分析课后习题答案1
时间序列分析课后习题答案(上机)
第二章
2、
(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:
(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:
(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)
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:
{
}的样本相关图:
该序列平稳,非白噪声。
第三章:
17、
(1)
结论:
序列平稳,非白噪声。
(2)拟合MA
(2)model:
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
80.40568
4.630308
17.36508
0.0000
MA
(1)
0.336783
0.114610
2.938519
0.0047
MA
(2)
0.343877
0.116874
2.942297
0.0046
R-squared
0.171979
Meandependentvar
80.29524
AdjustedR-squared
0.144379
S.D.dependentvar
23.71981
S.E.ofregression
21.94078
Akaikeinfocriterion
9.061019
Sumsquaredresid
28883.87
Schwarzcriterion
9.163073
Loglikelihood
-282.4221
F-statistic
6.230976
Durbin-Watsonstat
2.072640
Prob(F-statistic)
0.003477
InvertedMARoots
-.17+.56i
-.17-.56i
Residualtests
(3)拟合AR
(2)model:
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
79.71956
5.442613
14.64729
0.0000
AR
(1)
0.258624
0.128810
2.007794
0.0493
AR
(2)
0.227469
0.125114
1.818102
0.0742
R-squared
0.154672
Meandependentvar
79.50492
AdjustedR-squared
0.125522
S.D.dependentvar
23.35053
S.E.ofregression
21.83590
Akaikeinfocriterion
9.052918
Sumsquaredresid
27654.79
Schwarzcriterion
9.156731
Loglikelihood
-273.1140
F-statistic
5.306195
Durbin-Watsonstat
1.939572
Prob(F-statistic)
0.007651
InvertedARRoots
.62
-.36
Residualtests:
(4)拟合ARMA(2,1)model:
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
79.17503
4.082908
19.39183
0.0000
AR
(1)
-0.586834
0.118000
-4.973170
0.0000
AR
(2)
0.376120
0.082091
4.581756
0.0000
MA
(1)
1.113999
0.097122
11.47012
0.0000
R-squared
0.338419
Meandependentvar
79.50492
AdjustedR-squared
0.303599
S.D.dependentvar
23.35053
S.E.ofregression
19.48617
Akaikeinfocriterion
8.840611
Sumsquaredresid
21643.51
Schwarzcriterion
8.979029
Loglikelihood
-265.6386
F-statistic
9.719104
Durbin-Watsonstat
1.963688
Prob(F-statistic)
0.000028
InvertedARRoots
.39
-.97
InvertedMARoots
-1.11
EstimatedMAprocessisnoninvertible
残差检验:
(5)拟合ARMA(1,
(2))model:
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
79.52100
4.621910
17.20523
0.0000
AR
(1)
0.270506
0.125606
2.153603
0.0354
MA
(2)
0.233914
0.130773
1.788701
0.0788
R-squared
0.157273
Meandependentvar
79.55161
AdjustedR-squared
0.128706
S.D.dependentvar
23.16126
S.E.ofregression
21.61946
Akaikeinfocriterion
9.032242
Sumsquaredresid
27576.65
Schwarzcriterion
9.135167
Loglikelihood
-276.9995
F-statistic
5.505386
Durbin-Watsonstat
1.981887
Prob(F-statistic)
0.006423
InvertedARRoots
.27
残差检验:
(6)优化
model
AIC
SC
MA
(2)
9.0610
9.1631
AR
(2)
9.0529
9.1567
ARMA(2,1)
8.8406
8.9790
ARMA(1,
(2))
9.0322
9.1352
根据SC准则,最优模型为ARMA(2,1)模型。
(7)预测:
年份
预测值
标准差
95%的置信下限
95%的置信上限
1964
83.80630
19.48617
45.61341
121.9992
1965
88.05114
22.02801
44.87624
131.226
1966
75.70815
22.06639
32.45803
118.9583
1967
84.54800
22.28311
40.87310
128.2229
1968
74.71802
22.32277
30.96539
118.4706
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
Coefficient
Std.Error
t-Statistic
Prob.
C
0.845441
0.052013
16.25427
0.0000
AR
(1)
0.372564
0.111569
3.339322
0.0013
R-squared
0.135739
Meandependentvar
0.849589
AdjustedR-squared
0.123566
S.D.dependentvar
0.297627
S.E.ofregression
0.278633
Akaikeinfocriterion
0.309169
Sumsquaredresid
5.512162
Schwarzcriterion
0.371921
Loglikelihood
-9.284669
F-statistic
11.15107
Durbin-Watsonstat
2.068675
Prob(F-statistic)
0.001341
InvertedARRoots
.37
残差检验:
(3)拟合MA(6)model:
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
0.837270
0.065641
12.75526
0.0000
MA
(1)
0.201853
0.110289
1.830225
0.0715
MA
(2)
0.301118
0.104814
2.872875
0.0054
MA(4)
0.278566
0.110528
2.520322
0.0140
MA(6)
0.270084
0.115984
2.328636
0.0228
R-squared
0.189662
Meandependentvar
0.851216
AdjustedR-squared
0.142686
S.D.dependentvar
0.295913
S.E.ofregression
0.273989
Akaikeinfocriterion
0.313720
Sumsquaredresid
5.179833
Schwarzcriterion
0.469400
Loglikelihood
-6.607637
F-statistic
4.037420
Durbin-Watsonstat
1.867536
Prob(F-statistic)
0.005328
InvertedMARoots
.61+.50i
.61-.50i
-.04-.77i
-.04+.77i
-.68+.53i
-.68-.53i
残差检验:
(4)拟合ARMA(
(2),1)model
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
0.852299
0.061255
13.91390
0.0000
AR
(2)
0.260738
0.123711
2.107640
0.0387
MA
(1)
0.452777
0.117596
3.850279
0.0003
R-squared
0.219781
Meandependentvar
0.855139
AdjustedR-squared
0.197166
S.D.dependentvar
0.295887
S.E.ofregression
0.265118
Akaikeinfocriterion
0.223490
Sumsquaredresid
4.849841
Schwarzcriterion
0.318351
Loglikelihood
-5.045646
F-statistic
9.718346
Durbin-Watsonstat
2.041391
Prob(F-statistic)
0.000191
InvertedARRoots
.51
-.51
InvertedMARoots
-.45
残差检验:
(5)优化
model
AIC
SC
AR
(1)
0.3092
0.3719
MA(6)
0.3137
0.4694
ARMA(
(2),1)
0.2235
0.3184
根据SC准则,最优模型为ARMA(
(2),1)模型。
(6)预测:
年份
预测值
标准差
95%的置信下限
95%的置信上限
1975
0.64774
0.26512
0.12810
1.16737
1976
0.75001
0.29103
0.17960
1.32042
1977
0.79896
0.29912
0.21268
1.38524
1978
0.82563
0.30076
0.23615
1.41511
1979
0.83839
0.30130
0.24785
1.42893
18.
(1)
序列平稳,非白噪声
(2)拟合AR(3)模型:
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
84.13028
0.100370
838.2004
0.0000
AR
(1)
-0.395022
0.070460
-5.606293
0.0000
AR
(2)
-0.298634
0.072652
-4.110476
0.0001
AR(3)
-0.186335
0.070027
-2.660918
0.0084
R-squared
0.161289
Meandependentvar
84.12980
AdjustedR-squared
0.148320
S.D.dependentvar
2.877053
S.E.ofregression
2.655132
Akaikeinfocriterion
4.810861
Sumsquaredresid
1367.647
Schwarzcriterion
4.877291
Loglikelihood
-472.2752
F-statistic
12.43581
Durbin-Watsonstat
2.001728
Prob(F-statistic)
0.000000
InvertedARRoots
.06-.60i
.06+.60i
-.52
残差检验:
(3)拟合AR(1,2,3,6)模型:
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
84.14284
0.108789
773.4515
0.0000
AR
(1)
-0.395527
0.070754
-5.590134
0.0000
AR
(2)
-0.304273
0.073440
-4.143128
0.0001
AR(3)
-0.181864
0.070624
-2.575110
0.0108
AR(6)
0.148199
0.065240
2.271609
0.0242
R-squared
0.186539
Meandependentvar
84.13128
AdjustedR-squared
0.169414
S.D.dependentvar
2.889386
S.E.ofregression
2.633285
Akaikeinfocriterion
4.799648
Sumsquaredresid
1317.496
Schwarzcriterion
4.883571
Loglikelihood
-462.9657
F-statistic
10.89251
Durbin-Watsonstat
1.985492
Prob(F-statistic)
0.000000
InvertedARRoots
.59
.27-.71i
.27+.71i
-.37-.64i
-.37+.64i
-.79
残差检验:
(4)拟合MA
(1)模型:
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
84.13042
0.099045
849.4201
0.0000
MA
(1)
-0.480740
0.062375
-7.707312
0.0000
R-squared
0.148110
Meandependentvar
84.11940
AdjustedR-squared
0.143830
S.D.dependentvar
2.906625
S.E.ofregression
2.689485
Akaikeinfocriterion
4.826477
Sumsquaredresid
1439.433
Schwarzcriterion
4.859346
Loglikelihood
-483.0610
F-statistic
34.59833
Durbin-Watsonstat
1.872891
Prob(F-statistic)
0.000000
InvertedMARoots
.48
残差检验:
(5)拟合ARMA(
(1),(1,6))模型:
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
84.11553
0.126943
662.6253
0.0000
AR
(2)
-0.167970
0.074565
-2.252656
0.0254
MA
(1)
-0.375134
0.068739
-5.457376
0.0000
MA(6)
0.168123
0.065812
2.554578
0.0114
R-squared
0.175501
Meandependentvar
84.10402
AdjustedR-squared
0.162816
S.D.dependentvar
2.892726
S.E.ofregression
2.646779
Akaikeinfocriterion
4.804460
Sumsquaredresid
1366.061
Schwarzcriterion
4.870657
Loglikelihood
-474.0437
F-statistic
13.83572
Durbin-Watsonstat
2.001830
Prob(F-statistic)
0.000000
InvertedMARoots
.72-.36i
.72+.36i
.06+.73i
.06-.73i
-.59-.37i
-.59+.37i
残差检验:
(6)拟合ARMA(3,(6))模型:
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
84.12708
0.119520
703.8762
0.0000
AR
(1)
-0.388317
0.070662
-5.495430
0.0000
AR
(2)
-0.320461
0.072472
-4.421874
0.0000
AR(3)
-0.183754
0.070018
-2.624394
0.0094
MA(6)
0.227526
0.071453
3.184254
0.0017
R-squared
0.196499
Meandependentvar
84.12980
AdjustedR-squared
0.179846
S.D.dependentvar
2.877053
S.E.ofregression
2.605527
Akaikeinfocriterion
4.778075
Sumsquaredresid
1310.232
Schwarzcriterion
4.861112
Loglikelihood
-468.0294
F-statistic
11.79970
Durbin-Watsonstat
1.990809
Prob(F-statistic)
0.000000
InvertedARRoots
.05+.61i
.05-.61i
-.49
InvertedMARoots
.68+.39i
.68-.39i
.00-.78i
-.00+.78i
-.68+.39i
-.68-.39i
残差检验:
(7)优化
model
AIC
SC
AR(3)
4.8109
4.8773
AR(6)
4.7996
4.8836
MA
(1)
4.8265
4.8593
ARMA(2,6)
4.8045
4.8707
ARMA(3,6)
4.7781
4.8611
根据SC准则,最优模型为MA
(1)模型。
(8)预测:
预测值
标准差
95%的置信下限
95%的置信上限
202
85.69222
2.689485
80.42083
90.96361
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