时间序列分析课后习题答案1Word格式文档下载.docx
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时间序列分析课后习题答案1Word格式文档下载.docx
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(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:
50
100
150200250300350
(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:
1--=tttxxy{ty}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(2model:
Variable
CoefficientStd.Errort-StatisticProb.C80.405684.63030817.365080.0000MA(10.3367830.1146102.9385190.0047R-squared
0.171979Meandependentvar80.29524AdjustedR-squared0.144379S.D.dependentvar23.71981S.E.ofregression21.94078Akaikeinfocriterion9.061019Sumsquaredresid28883.87Schwarzcriterion9.163073Loglikelihood-282.4221F-statistic6.230976Durbin-Watsonstat2.072640Prob(F-statistic0.003477
Residualtests
(3拟合AR(2model:
C79.719565.44261314.647290.0000AR(1
0.258624
0.128810
2.007794
0.0493
R-squared
0.154672Meandependentvar79.50492AdjustedR-squared0.125522S.D.dependentvar23.35053S.E.ofregression21.83590Akaikeinfocriterion9.052918Sumsquaredresid27654.79Schwarzcriterion9.156731Loglikelihood-273.1140F-statistic5.306195Durbin-Watsonstat1.939572Prob(F-statistic0.007651
InvertedARRoots
.62
-.36
Residualtests:
(4拟合ARMA(2,1model:
VariableCoefficientStd.Errort-StatisticProb.C79.175034.08290819.391830.0000AR(1-0.5868340.118000-4.9731700.0000AR(20.3761200.0820914.5817560.0000MA(1
1.113999
0.097122
11.47012
0.0000
0.338419Meandependentvar79.50492AdjustedR-squared0.303599S.D.dependentvar23.35053S.E.ofregression19.48617Akaikeinfocriterion8.840611Sumsquaredresid21643.51Schwarzcriterion8.979029Loglikelihood
-265.6386F-statistic
9.719104
InvertedARRoots.39
-.97InvertedMARoots
-1.11
EstimatedMAprocessisnoninvertible
残差检验:
(5拟合ARMA(1,(2model:
VariableCoefficientStd.Errort-StatisticProb.C79.521004.62191017.205230.0000AR(10.2705060.1256062.1536030.0354R-squared
0.157273Meandependentvar79.55161AdjustedR-squared0.128706S.D.dependentvar23.16126S.E.ofregression21.61946Akaikeinfocriterion9.032242Sumsquaredresid27576.65Schwarzcriterion9.135167Loglikelihood-276.9995F-statistic5.505386Durbin-Watsonstat1.981887Prob(F-statistic0.006423
.27
(6优化
根据SC准则,最优模型为ARMA(2,1模型。
(7预测:
18、(1平稳性判断与纯随机性检验:
(2拟合AR(1model:
C0.8454410.05201316.254270.0000
R-squared0.135739Meandependentvar0.849589AdjustedR-squared0.123566S.D.dependentvar0.297627S.E.ofregression0.278633Akaikeinfocriterion0.309169Sumsquaredresid5.512162Schwarzcriterion0.371921Loglikelihood-9.284669F-statistic11.15107
InvertedARRoots.37
(3拟合MA(6model:
C0.8372700.06564112.755260.0000MA(10.2018530.1102891.8302250.0715MA(20.3011180.1048142.8728750.0054MA(40.2785660.1105282.5203220.0140MA(60.2700840.1159842.3286360.0228R-squared0.189662Meandependentvar0.851216AdjustedR-squared0.142686S.D.dependentvar0.295913S.E.ofregression0.273989Akaikeinfocriterion0.313720Sumsquaredresid5.179833Schwarzcriterion0.469400Loglikelihood-6.607637F-statistic4.037420Durbin-Watsonstat1.867536Prob(F-statistic0.005328InvertedMARoots.61+.50i.61-.50i-.04-.77i-.04+.77i-.68+.53i-.68-.53i
(4拟合ARMA((2,1model
VariableCoefficientStd.Errort-StatisticProb.
C0.8522990.06125513.913900.0000AR(20.2607380.1237112.1076400.0387MA(10.4527770.1175963.8502790.0003R-squared0.219781Meandependentvar0.855139AdjustedR-squared0.197166S.D.dependentvar0.295887S.E.ofregression0.265118Akaikeinfocriterion0.223490Sumsquaredresid4.849841Schwarzcriterion0.318351Loglikelihood-5.045646F-statistic9.718346Durbin-Watsonstat2.041391Prob(F-statistic0.000191InvertedARRoots.51-.51
InvertedMARoots-.45
(5优化
根据SC准则,最优模型为ARMA((2,1模型。
(6预测:
18.(1
序列平稳,非白噪声
(2拟合AR(3模型:
C84.130280.100370838.20040.0000AR(1-0.3950220.070460-5.6062930.0000AR(2-0.2986340.072652-4.1104760.0001AR(3-0.1863350.070027-2.6609180.0084R-squared0.161289Meandependentvar84.12980AdjustedR-squared0.148320S.D.dependentvar2.877053S.E.ofregression2.655132Akaikeinfocriterion4.810861Sumsquaredresid1367.647Schwarzcriterion4.877291Loglikelihood-472.2752F-statistic12.43581
InvertedARRoots.06-.60i.06+.60i-.52
(3拟合AR(1,2,3,6模型:
C84.142840.108789773.45150.0000AR(1-0.3955270.070754-5.5901340.0000AR(2-0.3042730.073440-4.1431280.0001AR(3-0.1818640.070624-2.5751100.0108
R-squared0.186539Meandependentvar84.13128AdjustedR-squared0.169414S.D.dependentvar2.889386S.E.ofregression2.633285Akaikeinfocriterion4.799648Sumsquaredresid1317.496Schwarzcriterion4.883571Loglikelihood-462.9657F-statistic10.89251Durbin-Watsonstat1.985492Prob(F-statistic0.000000InvertedARRoots.59.27-.71i.27+.71i-.37-.64i-.37+.64i-.79
(4拟合MA(1模型:
VariableCoefficientStd.Errort-StatisticProb.C84.130420.099045849.42010.0000MA(1-0.4807400.062375-7.7073120.0000R-squared0.148110Meandependentvar84.11940AdjustedR-squared0.143830S.D.dependentvar2.906625S.E.ofregression2.689485Akaikeinfocriterion4.826477Sumsquaredresid1439.433Schwarzcriterion4.859346Loglikelihood-483.0610F-statistic34.59833
InvertedMARoots.48
ARMA((1,(1,6模型模型:
(5)拟合ARMA((1,(1,6模型:
VariableCAR(2MA(1MA(6R-squaredAdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-WatsonstatInvertedMARootsCoefficient84.11553-0.167970-0.3751340.1681230.1755010.1628162.6467791366.061-474.04372.001830.72-.36i-.59-.37iStd.Error0.1269430.0745650.0687390.065812t-Statistic662.6253-2.252656-5.4573762.554578Prob.0.00000.02540.00000.011484.104022.8927264.8044604.87065713.835720.000000.06-.73i-.59+.37iMeandependentvarS.D.dependentvarAkaikeinfocriterionSchwarzcriterionF-statisticProb(F-statistic.72+.36i.06+.73i残差检验:
残差检验:
ARMA(3,(6模型模型:
(6)拟合ARMA(3,(6模型:
VariableCAR(1AR(2AR(3MA(6R-squaredAdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-WatsonstatInvertedARRootsInvertedMARootsCoefficient84.12708-0.388317-0.320461-0.1837540.2275260.1964990.1798462.6055271310.232-468.02941.990809.05+.61i.68+.39i-.68+.39iStd.Error0.1195200.0706620.0724720.0700180.071453t-Statistic703.8762-5.495430-4.421874-2.6243943.184254Prob.0.00000.00000.00000.00940.001784.129802.8770534.7780754.86111211.799700.000000MeandependentvarS.D.dependentvarAkaikeinfocriterionSchwarzcriterionF-statisticProb(F-statistic.05-.61i.68-.39i-.68-.39i-.49.00-.78i-.00+.78i
残差检验:
(7)优化modelAR(3AR(6MA(1ARMA(2,6ARMA(3,6AIC4.81094.79964.82654.80454.7781SC4.87734.88364.85934.87074.8611根据SC准则,最优模型为MA(1模型。
(8预测:
预测:
预测值20285.69222标准差2.68948595%的置信下限80.4208395%的置信上限90.96361
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