时间序列分析课后习题答案1

时间序列分析后习题案（上机）第二章2、342340338336334332330328197519761978

19791980（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）样本自相关系数：word档可自由复制编辑

（2）序列平稳。（3）Q统计量对应的概率均大于0.05，故接受该序列为噪声的假设，即序列为村随机序列。5）时序图和样本自相关图：3503002502001501005000:0100:0701:0101:0702:0102:0703:0103:07Xword档可自由复制编辑

（2）序列具有明显的周期性，非平稳。（3）序列的Q计量对应的概率均小于，该序列是非白噪声的。6）word档可自由复制编辑

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yxtt{y}样本相关图：t

t该序列平稳，非白噪声。第三章：

1word档可自由复制编辑

结论：序列平稳，非白噪声。（2）拟合MA(2)model:VariableCMA(1)MA(2)

Coefficient80.405680.3367830.343877

Std.Error4.6303080.1146100.116874

t-Statistic17.365082.9385192.942297

Prob.0.00000.00470.0046R-squared

0.171979Meandependentvar80.29524AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-WatsonstatInvertedMARootsResidual

0.144379S.D.dependentvar21.94078Akaikeinfocriterion28883.87Schwarzcriterion-282.4221F-statistic2.072640Prob(F-statistic)-.17+.56i-.17-.56i

23.719819.0610199.1630736.2309760.003477（）拟合AR(2)model：VariableCAR(1)

Coefficient79.719560.258624

Std.Error5.4426130.128810

t-Statistic14.647292.007794

Prob.0.00000.0493word档可自由复制编辑

AR(2)R-squared

0.2274690.1251141.8181020.07420.154672Meandependentvar79.50492AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-WatsonstatInvertedARRootsResidual

0.125522S.D.dependentvar21.83590Akaikeinfocriterion27654.79Schwarzcriterion-273.1140F-statistic1.939572Prob(F-statistic).62-.36

23.350539.0529189.1567315.3061950.007651(4)拟合，1）：VariableCAR(1)AR(2)MA(1)

Coefficient79.17503-0.5868340.3761201.113999

Std.Error4.0829080.1180000.0820910.097122

t-Statistic19.39183-4.9731704.58175611.47012

Prob.0.00000.00000.00000.0000R-squared

0.338419Meandependentvar79.50492AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodword档可自由复制编辑

0.303599S.D.dependentvar19.48617Akaikeinfocriterion21643.51Schwarzcriterion-265.6386F-statistic

23.350538.8406118.9790299.719104

Durbin-WatsonstatInvertedARRootsInvertedMARoots残差检验：

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

0.000028（）拟合12）model:VariableCAR(1)MA(2)

Coefficient79.521000.2705060.233914

Std.Error4.6219100.1256060.130773

t-Statistic17.205232.1536031.788701

Prob.0.00000.03540.0788R-squared

0.157273Meandependentvar79.55161AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-WatsonstatInvertedARRoots残差检验：

0.128706S.D.dependentvar21.61946Akaikeinfocriterion27576.65Schwarzcriterion-276.9995F-statistic1.981887Prob(F-statistic).27

23.161269.0322429.1351675.5053860.006423word档可自由复制编辑

(6)化modelMA(2)AR(2)ARMA(2，1)ARMA(1,（2）)

AIC9.06109.05298.84069.0322

SC9.16319.15678.97909.1352根据SC准则，最优模型为ARMA(2,1)模型。(7)测：年份

预测值

标准差

95％的置信下限95％的置信上限19641965196619671968

83.8063088.0511475.7081584.5480074.71802

19.4861722.0280122.0663922.2831122.32277

45.6134144.8762432.4580340.8731030.96539

121.9992131.226118.9583128.2229118.4706word档可自由复制编辑

18）平稳性判断与纯随机性检验：序列平稳，非白噪声。（）拟合）model:VariableCAR(1)

Coefficient0.8454410.372564

Std.Error0.0520130.111569

t-Statistic16.254273.339322

Prob.0.00000.0013R-squared

0.135739Meandependentvar0.849589AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-WatsonstatInvertedARRoots残差检验：

0.123566S.D.dependentvar0.278633Akaikeinfocriterion5.512162Schwarzcriterion-9.284669F-statistic2.068675Prob(F-statistic).37

0.2976270.3091690.37192111.151070.001341word档可自由复制编辑

（）拟合）model:VariableCMA(1)MA(2)MA(4)MA(6)

Coefficient0.8372700.2018530.3011180.2785660.270084

Std.Error0.0656410.1102890.1048140.1105280.115984

t-Statistic12.755261.8302252.8728752.5203222.328636

Prob.0.00000.07150.00540.01400.0228R-squaredAdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-Watsonstat

0.189662Meandependentvar0.142686S.D.dependentvar0.273989Akaikeinfocriterion5.179833Schwarzcriterion-6.607637F-statistic1.867536Prob(F-statistic)

0.8512160.2959130.3137200.4694004.0374200.005328InvertedMARoots残差检：

.61+.50i.61-.50i-.04-.77i-.04+.77i-.68+.53i-.68-.53iword档可自由复制编辑

（）拟合ARMA((2),1)modelVariableCAR(2)MA(1)

Coefficient0.8522990.2607380.452777

Std.Error0.0612550.1237110.117596

t-Statistic13.913902.1076403.850279

Prob.0.00000.03870.0003R-squared

0.219781Meandependentvar0.855139AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-WatsonstatInvertedARRootsInvertedMARoots残差检：

0.197166S.D.dependentvar0.265118Akaikeinfocriterion4.849841Schwarzcriterion-5.045646F-statistic2.041391Prob(F-statistic).51-.51-.45

0.2958870.2234900.3183519.7183460.000191word档可自由复制编辑

（）优化modelAR(1)MA(6)ARMA((2)，1)

AIC0.30920.31370.2235

SC0.37190.46940.3184根据SC准则，最优模型为ARMA((2),1)模型。(6)测：年份

预测值

标准差

95％的置信下限95％的置信上限19751976197719781979

0.647740.750010.798960.825630.83839

0.265120.291030.299120.300760.30130

0.128100.179600.212680.236150.24785

1.167371.320421.385241.415111.42893word档可自由复制编辑

18.(1)序列平，非白噪声（）拟合）模型VariableCAR(1)AR(2)AR(3)

Coefficient84.13028-0.395022-0.298634-0.186335

Std.Error0.1003700.0704600.0726520.070027

t-Statistic838.2004-5.606293-4.110476-2.660918

Prob.0.00000.00000.00010.0084R-squared

0.161289Meandependentvar84.12980AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-WatsonstatInvertedARRootsword档可自由复制编辑

0.148320S.D.dependentvar2.655132Akaikeinfocriterion1367.647Schwarzcriterion-472.2752F-statistic2.001728Prob(F-statistic).06-.60i.06+.60i-.52

2.8770534.8108614.87729112.435810.000000

残差检：（）拟合AR(1,2,3,6)型：VariableCAR(1)AR(2)AR(3)AR(6)

Coefficient84.14284-0.395527-0.304273-0.1818640.148199

Std.Error0.1087890.0707540.0734400.0706240.065240

t-Statistic773.4515-5.590134-4.143128-2.5751102.271609

Prob.0.00000.00000.00010.01080.0242R-squared

0.186539Meandependentvar84.13128AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-Watsonstat

0.169414S.D.dependentvar2.633285Akaikeinfocriterion1317.496Schwarzcriterion-462.9657F-statistic1.985492Prob(F-statistic)

2.8893864.7996484.88357110.892510.000000InvertedARRootsword档可自由复制编辑

.59.27-.71i.27+.71i-.37-.64i-.37+.64i-.79

残差检：（）拟合）模型VariableCMA(1)

Coefficient84.13042-0.480740

Std.Error0.0990450.062375

t-Statistic849.4201-7.707312

Prob.0.00000.0000R-squared

0.148110Meandependentvar84.11940AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-WatsonstatInvertedMARoots残差检：

0.143830S.D.dependentvar2.689485Akaikeinfocriterion1439.433Schwarzcriterion-483.0610F-statistic1.872891Prob(F-statistic).48

2.9066254.8264774.85934634.598330.000000word档可自由复制编辑

（）拟合ARMA((1),(1,6))模型：VariableCAR(2)MA(1)MA(6)

Coefficient84.11553-0.167970-0.3751340.168123

Std.Error0.1269430.0745650.0687390.065812

t-Statistic662.6253-2.252656-5.4573762.554578

Prob.0.00000.02540.00000.0114R-squared

0.175501Meandependentvar84.10402AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-Watsonstat

0.162816S.D.dependentvar2.646779Akaikeinfocriterion1366.061Schwarzcriterion-474.0437F-statistic2.001830Prob(F-statistic)

2.8927264.8044604.87065713.835720.000000InvertedMARoots残差检：

.72-.36i.72+.36i.06+.73i.06-.73i-.59-.37i-.59+.37iword档可自由复制编辑

（）拟合ARMA(3(6))模：VariableCAR(1)AR(2)AR(3)MA(6)

Coefficient84.12708-0.388317-0.320461-0.183