非平稳时间序列分析汇编.docx

非平稳时间序列分析汇编.docx

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非平稳时间序列分析汇编

非平稳时间序列分析

1、首先画出时序图如下：

从时序图中看出有明显的递增趋势，而该序列是一直递增，不随季节波动，所以认为该序列不存在季节特征。

故对原序列做一阶差分，画出一阶差分后的时序图如下：

从中可以看到一阶差分后序列仍然带有明显的增长趋势，再做二阶差分：

做完二阶差分可以看到，数据的趋势已经消除，接下来对二阶差分后的序列进行检验：

Autocorrelations

LagCovarianceCorrelation-198765432101234567891StdError

0577.3331.00000||********************|0

1-209.345-.36261|*******|.|0.071247

2-52.915660-.09166|.**|.|0.080069

39.1391950.01583|.|.|0.080600

415.3758920.02663|.|*.|0.080615

5-59.441547-.10296|.**|.|0.080660

6-23.834489-.04128|.*|.|0.081324

7100.2850.17370|.|***|0.081431

8-146.329-.25346|*****|.|0.083290

952.2286580.09047|.|**.|0.087118

1021.0085750.03639|.|*.|0.087593

11134.0180.23213|.|*****|0.087670

12-181.531-.31443|******|.|0.090736

1323.2684700.04030|.|*.|0.096108

1471.1121950.12317|.|**.|0.096194

15-105.621-.18295|****|.|0.096991

1637.5919960.06511|.|*.|0.098727

1723.0315060.03989|.|*.|0.098945

1845.6547450.07908|.|**.|0.099027

19-101.320-.17550|****|.|0.099347

20127.6070.22103|.|****|0.100908

21-61.519663-.10656|.**|.|0.103337

2235.8253170.06205|.|*.|0.103893

23-93.627333-.16217|.***|.|0.104081

2455.4512080.09605|.|**.|

从其自相关图中可以看出二阶差分后的序列自相关系数很快衰减为零，且都在两倍标准差范围之内，所以认为平稳，白噪声检验结果：

AutocorrelationCheckforWhiteNoise

ToChi-Pr>

LagSquareDFChiSq--------------------Autocorrelations--------------------

630.706<.0001-0.363-0.0920.0160.027-0.103-0.041

1284.5412<.00010.174-0.2530.0900.0360.232-0.314

1897.9818<.00010.0400.123-0.1830.0650.0400.079

24126.9924<.0001-0.1750.221-0.1070.062-0.1620.096

P值都小于0.05，认为不是白噪声。

接下来对模型进行定阶：

MinimumInformationCriterion

LagsMA0MA1MA2MA3MA4MA5

AR06.3569056.1418316.1498386.1755526.1915646.203649

AR16.2369226.1681216.151526.1726746.1869626.193905

AR26.1932156.1808186.1773376.1974076.2032246.207239

AR36.197486.2030816.2028376.2210836.2153136.188712

AR46.2203136.229496.2274456.2418836.1628376.189358

AR56.2221316.2367396.2440256.2649686.1859636.210425

Errorseriesmodel:

AR（10）

MinimumTableValue:

BIC（0,1）=6.141831

从sas的定阶结果来看，BIC（0,1）取得最小值，所以选取MA

（1）模型，接下来对模型进行拟合：

得到模型为：

模型检验结果为：

ConditionalLeastSquaresEstimation

StandardApprox

ParameterEstimateErrortValuePr>|t|Lag

MU0.402860.169002.380.01810

MA1,10.890630.0326627.27<.00011

检验结果显示都显著。

接下来利用此模型对1997年的四个季度进行预测：

Forecastsforvariablex

时间ForecastStdError95%ConfidenceLimits

1997一季度7759.206131.22767698.00117820.4112

1997二季度7842.613540.30487763.61757921.6095

1997三季度7926.423748.94447830.49458022.3530

1997四季度8010.636857.43567898.06518123.2085

预测图：

本题代码

dataaa;

inputx@@;

difx=dif（x）;

dif2x=dif（difx）;

t=intnx（'quarter','1jan1947'd,_n_-1）;

formattyear4.;

cards;

227.8231.7236.1246.3252.6259.9266.8268.1263.0

259.5261.2258.9269.6279.3296.9308.4323.2331.1

337.9342.3345.3345.9351.7364.2371.0374.5373.7

368.7368.4368.7373.4381.9394.8403.1411.4417.8

420.5426.0430.8439.2448.1450.1457.2451.7444.4

448.6461.8475.0499.0512.0512.5516.9530.3529.2

532.2527.3531.8542.4553.2566.3579.0586.9594.1

597.7606.8615.3628.2637.5654.5663.4674.3679.9

701.2713.9730.4752.6775.6785.2798.6812.5822.2

828.2844.7861.2886.5910.8926.0943.6966.3979.9

999.31008.01020.31035.71053.81058.41104.21124.91144.4

1158.81198.51231.81256.71297.01347.91379.41404.41449.7

1463.91496.81526.41563.21571.31608.31670.61725.31783.5

1814.01847.91899.01954.52026.42088.72120.42166.82293.7

2356.22437.02491.42552.92629.72687.52761.72756.12818.8

2941.53076.63105.43197.73222.83221.03270.33287.83323.8

3388.23501.03596.83700.33824.43911.33975.64022.74100.4

4158.74238.84306.24376.64399.44455.84508.54573.14655.5

4731.44845.24914.55013.75105.35217.15329.25423.95501.3

5557.05681.45767.85796.85813.65849.05904.55959.46016.6

6138.36212.26281.16390.56458.46512.36584.86684.56773.6

6876.36977.67062.27140.57202.47293.47344.37426.67537.5

7593.6

;

procgplot;

plotx*tdifx*tdif2x*t;

symbolc=blacki=joinv=star;

run;

procarima;

identifyvar=x（1,1）nlag=8minicp=（0:

5）q=（0:

5）;

estimateq=1;

forecastlead=5id=tinterval=quarterout=results;

run;

procgplotdata=results;

plotx*t=1forecast*t=2l95*t=3u95*t=3/overlay;

symbol1c=blacki=nonev=star;

symbol2c=redi=joinv=none;

symbolc=greeni=joinv=nonel=32;

run;

2、首先画出时序图：

从时序图中可以看出序列存在递增趋势，而且存在季节性特征，接下来对序列进行一阶差分，画出差分后的时序图：

可以看到趋势已经消除，但季节性仍存在，对其进行检验：

Autocorrelations

LagCovarianceCorrelation-198765432101234567891StdError

016681.7471.00000||********************|0

1-3098.631-.18575|****|.|0.049568