时间序列分析课后习题答案1.docx

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、

328

330332334336338340

342

（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:

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

R-squared

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

InvertedARRoots

.27

残差检验:

（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:

序列平稳,非白噪声。

（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

残差检验:

（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

残差检验:

（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

残差检验:

（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:

VariableCoefficientStd.Errort-StatisticProb.

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

残差检验:

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：

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