王燕时间序列分析第五章SAS程序.docx

1、王燕时间序列分析第五章SAS程序第一题data yx_51;input x;difx=dif(x);t=l+_n_-l;cards;304 303 307 299 296 293 301 293 301 295 284 286 286 287 284 282 278 281278 277 279 278 270 268 272 273 279 279 280 275 271277 278 279 283284 282 283 279 280 280 279 278 283 278 270 275 273 273 272 275 273273 277 274 274 272 280 282 29

2、2 295 295 294 290 291 288 288 290 293 288289 Z91 293 293 290 288 287 Z89 292 288 288 285 282286 286 287 284283 286 282 287 286 287 292 292 294 291 2882899procgplot;plot x*t=ldifx*t=2;symbo1lc=red v=circle i=join;symbo12c=ye11ow v=star i=join;run;procarima;identifyvar=x(1);estimatep=l;run;结果如下 时序图：-阶

3、差分后时序图:di fi10-102010 2030 40 50 60 706090 100 110SAS系统2014年05月06日星期二 下午10时47分58秒 1The ARI MA ProcedureName of Variable = xPeriod(s) of DifferencingMean of forking SeriesStandard DeviationNumber of ObservationsObservation(s) eliminated by differenci1-0.141513.6145371061Autocorrelat ionsStd Error0113

4、.064881-2.0202141.00000 -.1548320.2518470.019283-0.803468-.063154-1.166473-.089285-0.407940-.03122 *61.3663630.10463榊：72.4610310.188378-0.727748-.05570:務90.6224540.04764 :10-1.716200-.13136出林110.8241060.06308* :120.1365720.01045130.6362800.04097.14-1.830163-.14008152.0025060.15327曲16-1.865607-.14280

5、17-0.53560704100 *180.8495720.06503*190.4733600.03623200.5607460.04292* ,21-2.6024901992022-0.104103-.0079723-0.666324-.05100 *24-0.537108-.04111 Lag CovarianceCorrelation1 9 8 7 6 5 4 3 2 10 12 3 4 5 6 7 8 9 1marks two stand&rd errors0.037129 0.099424 0.039458 0.099912 0.100662 0.100753 0.101773 0.

6、105010 0.105289 0.105492 0.107024 0.107374 0.107384 0.107531 0.109239 0.111249 0.112965 0.113106 0.113458 0.113567 0.113720 0.116965 0.116970 0.1171802ai405H06tl 星期二 I、午 10旳47甘58抄 2Inverse Autocorrelations120.12567 -0.0592930.0240240.17471*K.50.03817来60.17242 ； 冷肾；?-0.219D680.08852佛岀9-0.0167110-0.00

7、15711-0.09685榊120.01518130.09241删.140.06628* 15-0.18306H4nh*160.079641?0.08334180.01169Lftg Correlftt ionSAS糸统The ARINA Procedure19-0.05799 #200.01034210.1762&220.08267桝.230.01342240.06638* .Correlat ion2-19 83 4 5 6 7 8 9 1Partial Autocorrelat ions1-0.154632-0.004753-0.06853 *4-0.113595-0.06560 *60

8、.0874270.215518-0.0048290.04333 100.07757110.07S3&120.0403413-0.0023714-0.19934150.12464榊：16-0.03053:*17-0.06859.*18-0.01418190.06543 200.0654421-0.1841822-0.12096230.0434024-0.08493Lag Correlat ionAutocorrelation Check for White NoiseToLac612IS24Ch卜Square5.4412.7221.6928.05DF6121824Pr ChiSq0.48300.

9、38960.24620.2579A 1 | _ -0.155 0.0190.188 -0.0560.041 -0.1400.036 0.043Hutuuur rciat imi3-0.0310.063-0.041-0.0510.1050.0100.065 -0.041-0.0690.0480.153 -0.199-0.088-0.131-0.143-0.008Conditional Least SquaresEstimationStandardApproxParatneterEstimateError t:ValuePr ItlLagMU-0.142010.30359-0.470.64090A

10、R1,1-0.154780.09692-1.600.11331The ARIMA Procedure-0.1639312.987443.605196574.6596579.9865106log determinantConstant Est imateVar ianee Est iinateSid Error EstimateAICSBCNumber of Residuals AIC and SBC do not includeCor re I at ions of Pa.rameterEstimatesTo LagChi-SquareDFPr ChiSqAux ocorre 1ationse

11、4.3150.5056-0.0010.0150.0830.110-0.0300.1341211.35110.41480.205-0.0210.020-0.1200.Q470.0281818.00170.38890.023-0.1160.116-0.132-0.0550.0682425.30230.33520.0550.020-0.204-0.048-0.0610.054Autocorrelation Check ofResiduals-0.142011Est imated MeanPeriod(s) of D i f ferenc iAutoregressive FactorsFactor 1

12、： 1 + 0.15478 B(1)通过原始数据的时圧图可以明显看出，此圧列非平稳，因而对丿子列进行一阶 差分。从一阶差分后的自相关图可以看出，一阶差分后的序列的门相关系数一直 都比较小，始终控制在二倍标准差以内，可以认为一阶差分后的序列始终都在零 轴附近波动，冈而可以认为一阶差分后的序列为随机性很强的平稳仔列，另外通 过一阶差分后的时序图也可以看出，一阶差分后的序列半稳，且LB统计最对应 的P值大于a =0.05,因而认为一阶差分后的序列为白噪声序列。由于一阶差分后的字列为平稳的白噪声斥列，因而此时间序列拟合ARIMA （0.1,0）模型，即随机游走模型，模型为：&訓1+&所以下一期的预测值

13、为289第二题data yx_52; input x; t=1949+_n_-l; difx=dif(x); cards;5589.0019376.9983 0000 24605.11083.000013217.0016131.0019288.0027421 0038109.0054410.0067219.0044988.0035261.0036418.00 41786.0049100.0054951 0043089.0042095.0053120 0068132 0076471.00 80873.0083111.0078772.0088955.0084066.0095309.00110119

14、.00111893 00 111279 00107673.00113495.00118784.00124074.00130709 00135635.00140653.00 144948.00151489.00150681 00152893 00157627.00162794.00163216.00165982.00 171024.00172149.00164309.001675S4.00178581.00193189 00204956.00224248.00 249017.0026929600288224.00314237.00330354.00procgplot;plot x*t=ldifx

15、*t=2;symbollc=orange v=circle i=none; symbol2c=blue v=star i=join; procarima;iderrtifyvaf=x (1);estimateq=l;forecastiead=5id=t;时序图:400000300000200000100000iao 1W0 1%0 1970 19c 1990 2000 2010t从时序图可以看出，时间序列非平稳，且随着时间而呈现明显的上升趋势, 因而对序列采用一阶差分：一阶差分后的时序图：2014年05月07曰星期三下午11时03分5?秒SAS系统The AR I MA ProcedureNa

16、me of Variable = xPeriod(s) of Differncing; 1Mean of Work!ng Series 5504.492Standard Devi at ion 8441.125Number of Observat i ons 59Observation(s) eIiminated by differencing 1Autocorrelat ions0712525931.0000001360409150.50582欢脚脚脚出紂0.1901892117143630.164410.160069352602170.07382* 0.162906480009270.11

17、229 0.163472597464490.13679溶榊 0.1647746123345980.17311*SW .0.166688738193180.05360* 0.1697088-10165750-.14267 氷榊0.1688949-11251547-.157910.17201210-6251580-.087740.17445211-1171287-.016440.1751981238508960.054050.1752241317864240.0250? 0.17550614-1315326-.018460.175567Lag CovarianceCorrelat ion-1 98

18、765432101234567891Std Errormarks two standard errorsInverse 占utocorrelat ions-0.452230.0 舲 65芈寧屮*宋出屮昭卑0.04221-0.13557柑*0.07544-0.081840.079170.15808*-0.02016100.00599110.0599312-0.08m190.04124出14-0.02919Part i a I 右utocorre I at i ons120.50582 -0.1228930.05813出 40.0904450.05040出 .60.103967-0.113638-

19、0.18030SAS务统 201405月07日星期三下午11时03分57秒 2The ARIMA ProcedurePartial Autocorrelations9-0.0047310-0.02212110.02688120.0873513-0.01434140.0395815Autocorrelat ion Check for White NoiseParameterEst inciteStandardErrort ValueApproxPr ItlLagMU5536.61430.13.870.00030MA1,1-0.483490.11623-4.160.00011Condi t ion

20、aILeast Squares Estimation* AIC and SBC do not incIude log deterninant.Constant Estimate 553665 Variance Estimate 55720793 Std Error Estimate 7464.636 AIC 1221.716 S8C 1225.871 Number of Residuals 59Correlations of ParaneterEst i mfttesParameterMUMALIMU1.0000.003MAI J0.0031.000ResidualsAutocorrelat

21、ion Check ofToLacChi- SquareDFPr ChiSq ocorreiatiode 64.6950.45520.0940.156-0.0220.1150.0500.151127.25110.77850.0530.132-0.097-0.046-0.0260.058189.33I70.92940.023-0.0490.048-0.112-0.0440.0702410.67230.98630.088-0.030-0.0710.013-0.023-0.00?5536.65EstI mated Mean.Period(s) of DifferencingSAS系裁 201405月

22、07曰星期三下午II时03分57秒 6The ARINA ProcedureMoving Average FactorsFactor 1: 1 4 0.48349Forecasts for variable xObsForecastStd Error95X Conf i dence Limits61337276.98377464.6361322646.5657351907.401762342813.633613354.667316638.9669368988.300463348350283617348.58?314347.6774382352.888864353886.933620581.54

23、1313547.8548394226.012385359423.583523371.482313G1G.32O8405230.8463通过原始数据的时用图可以明显看出，此序列非平稳，随着时间呈现上升趋势, 因而对序列进行一阶差分。从一阶差分后的H相关图可以看出，一阶差分后的序 列的自相关系数一阶截尾，拟合ARIMA(0, 1, 1)模型，得到模型：XrXt.i=(H-0.48349B) e t残差的检验显示，残差序列通过白噪声检验，参数显苦性检验显示参数显著:，说 明模型拟合良好，对序列相关信息提取充分。得到20092013年铁路货运最的预测结果如下：铁路货运与测量2009337276.983

24、72010342813.63362011348350.283620123538X693362013359423.5835第三题;data yx_53;input x;difx=dif(dif12(x);t=intnx (fmonth19 f01janl973 fdr _n_-l); formattdate ;cards;9007.00 8106.00 8528.0011317. 00 10744.009713.009938 009161 008038.008422.008714.10120.009823.008743.008162.007306.008124.7870.009387.009SS

25、6 008433.008160.008034.7717.00 7461.00 7776 0010078 00 9179 008037.8488.00 7874. 008647.008106.00 8890.009299.9302.00 8314.008850.006892.00 7791 008129.9434.00 10484.009827.009240.009137.0010017.0010826.008927 007750.006981.00009512.DO9129.008710.008680.000010093.009620.008285.00007925.008634.008945.00007792.00