王燕时间序列分析第五章SAS程序

282278281271277278279283284282283275280280279278283278270275273273272275273第一题datayx_51;inputx@@;difx=dif(x);t=l+_n_-l;cards;304303282278281271277278279283284282283275280280279278283278270275273273272275273278277279278270268272273279275280275273272273272273271272271273277274274272280282292295295273277274274272280282292295295294290291288288290253288289291293293290288287289292288288285282286286287284283286282287286287292292294291288289procgplot;plotx*t=ldifx*t=2;symbollc=redv=circlei=join;svmbo【Zc=yell.owv=stari=join;run;procarima;identifyvar=x(1);estimatep=l;run;结果如下时序图：difx10--10--20-1020304050607080901C0110TOC\o"1-5"\h\zSAS系统201徊05月06曰星期二下午10时47分58秒1TheARIMAProcedureNameofVariable=xPeriod(s)ofDifferencing1MeanofWorkingSeries-0.14151StandardDeviation3.614537NumberofObservations106Observation(s)eliminatedbydifferencing1Autocorrelations0113.064881-2.0202141.00000-.15463.###qiinipipipipipipipipiprpipipipipipip00.09712920.2518470.019280.0994243-0.303468-.06915:H60.0384584-1.166473-.089280.0999125-0.407940-.03122・*0.10066261.3669680.10463出出：0.10075372.4610310.18837帆**0.1017738-0.727748-.05570:溶0.10501090.6224540.04764*:0.10528910-1.716200-.13136.###0.105492110.8241060.06308卅：0.107024120.1365720.010450.107374130.5352800.04097卅：0.10738414-1.830163-.14008.###0.107531152.0025060.153270.10923916-1.86560?-.14280.###0.1112491?-0.535607-.04100・此0.112965180.8495720.06503*:0.113106190.4733600.03623卅・0.113458200.5607460.04292卅・0.11356?21-2.602490-.199200.11372022-0.104103-.007970.11696523-0.666324-.05100:北0.11697024-0.537108-.04111・«0.117180CovarianceCorrelation-198765432101234567891StdErrormarkstwostandarderrors

LagCorrelation-•1987654321()123456789110.125672-0.05929:*30.Q240240.1747150.038176-0.172427-0.2190680.08852脚.9-0.0167110-0.0015711-0.09685:榔120.01518130.09241院：140.0652815-0.18306160.Q7964170.08334林.180.Q1168SAS条貌”14年05月06”14年05月06口星期二卜午10射4?行58杪2CorreIation■■198765432101234567891-0.05799・*.0.01034.0.176260.08267-0.0134200.08638PartialAutocorrelationsjorrelation-•1987654321()1234567891-0.15463.m-0.00475-0.06853・*-0.11359-0.06560・«0.087420.21551****-0.004820.04333-0.077570.078360.04084-0.00237-0.199340.12464林：-0.09053:榔-0.08859.米-0.014180.065430.06544-0.18418娜娜-0.120960.04340-0.08493Lag192021222324Lag123456789101112131415161718192021222324ParameterMUAR1,1ConditionalEstimate-0.14201-0.15478LeastStandardErrortValueApproxPr>ItlLag0.30359-0.470.640900.09692-1.600.11331SquaresEstimationTheARIMAProcedureConstantEstParameterMUAR1,1ConditionalEstimate-0.14201-0.15478LeastStandardErrortValueApproxPr>ItlLag0.30359-0.470.640900.09692-1.600.11331SquaresEstimationTheARIMAProcedureConstantEstimateVarianceEstimateSidErrorEstirnateAICSBCNumberofResidualsAICandSBCdonotinclude-0.1639912.997443.605196574.6596579.9885106logdeterminant.CorreIationsofParameter

EstimatesParameterMUAR1,1MUARIJ1.0000.0030.0031.000ToChi-Pr>LagSquareDFChiSqAuiocorre1alions64.3150.5056-0.001-0.015-0.083-0.110-0.0300.1341211.35110.41480.205-0.0210.020-0.1200.0470.0281818.00170.38890.023-0.1160.116-0.132-0.0550.0682425.30230.33520.0550.020-0.204-0.048-0.061-Q.054AutocorrelationCheckofResidualsModeIforvariableEstimatedMeanPeriod(s)ofDifferencing:-0.14201AutoregressiveFactorsFactor1：14-0.15478B^(1)通过原始数据的时序图可以明显看出，此序列非平稳，因而对序列进行一阶差分。从一阶差分后的自相关图可以看出，一阶差分后的序列的自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，因而可以认为一阶差分后的序列为随机性很强的平稳序列，另外通过一阶差分后的时序图也可以看出，一阶差分后的序列平稳，且LB统计量对应ToLagChi-SquareDFPr>ChiSqAutocorrelations65.4460.4890-0.1550.019-0.069-0.089-0.0310.1051212.72120.38960.188-0.0560.048-0.1310.0630.0101821.69180.24620.041-0.1400.153-0.143-0.0410.0652428.05240.25790.0360.043-0.199-0.008-0.051-0.041

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。由于一阶差分后的序列为平稳的白噪声序列，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：Xt=Xt_i+&所以下一期的预测值为289第二题datayx_52;inputx@@;t=1949+_n_-l;difx=dif(x);cards;5589.009983.0011083.0019376.0024605.0027421.0038109.0054410.0036418.0041786.0049100.0054951.0043089.0076471.0080873.0083111.0078772.0088955.00111853.00111279.00107673.00113495.00118784.00140653.00144948.00151489.00150681.00152853.00165982.00171024.00172149.00164309.00167554.00224248.00245017.00269296.00288224.00314237.0013217.0067219.0042095.0084066.00124074.00157627.00178581.00330354.0016131.0044988.0053120.0095309.00130709.00162794.00193189.0019288.0035261.0068132.00110119.00135635.00163216.00204956.00procgplot;plot5589.009983.0011083.0019376.0024605.0027421.0038109.0054410.0036418.0041786.0049100.0054951.0043089.0076471.0080873.0083111.0078772.0088955.00111853.00111279.00107673.00113495.00118784.00140653.00144948.00151489.00150681.00152853.00165982.00171024.00172149.00164309.00167554.00224248.00245017.00269296.00288224.00314237.0013217.0067219.0042095.0084066.00124074.00157627.00178581.00330354.0016131.0044988.0053120.0095309.00130709.00162794.00193189.0019288.0035261.0068132.00110119.00135635.00163216.00204956.001"19501彻197019的199020002010t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：^0012345678901234SAS系统TheARIMAProcedureNameofVariable=xPeriod(s)ofDifferencingMeanofWorkingSeriesStandardDeviationNumberofObservationsObservation(s)eliminatedbydifferencing201徊05月0?曰15504.4928441.125591星期三下午11时03分57秒AutocorrelationsCovarianceCorrelation-•1987654321(1234567891StdError712525933804091511714363526021780009279746449123345883819318-10165750-1125154?-6251580-117128?38508961786424-13153261.000000.505820.164410.073820.112290.136790.173110.05360-.14267-.15791-.08774-.016440.054050.0250?-.01846..m・娜<!•*1*•»,•»,<1*•»,*»••»,•■•<1*•»,ilfibilfibalfilfilfilBilfibQIQIQIfljeQIQIQI溯帆・溯・溯卅・溯帆・溯・*:溯・00.1301890.1600690.1629060.1634720.1647740.1666880.1697080.1698940.1720120.1744520.1751980.1752240.1755060.175567markstwostandarderrorsg12345678901234Correlation-198785432101234587891-0.452230.083650.04221*.-0.13657・相^0.07544卅卅：-0.08184・*出-0.07917・娜0.15808-0.02016Q.005930.05993:■Q.088830.04124:-0.02819.出PartialAutocorrelationsCorrelation•198785432101234587891InverseAutocorrelations0.50582-Q.122890.058130.090440.050400.10396-0.11363-0.18030.脚出.用出■出.用出■・歌出SAS系统TheARIMAProcedurePartialAutocorrelations9-0.0047310-0.02212110.02688卅：120.0873513-0.01434140.03958卅：LagCorrelation-198765432101234567891AutocorrelationCheckforWhiteNoiseToLagChi-SquareDFPr>pu；O-Un1BqAutocorreiations--61222.0426.286120.00120.5060.1640.00980.054-0.1430.074-0.1580.112-0.0880.137-0.0160.1730.054Conditiona1LeastSquaresEstimationParameterStandardEstimateErrortValueApproxPr>|t|LagMUMAI,15536.61430.1-0.483490.116233.8?-4.160.00030.000101ConstantEstimateVarianceEstimateStdErrorEstimateAICSBCNumberofResiduals卅AICandSBCdonotinc1ude5536.65557207937464.6361221.7161225.87159logdeterminant.CorrelationsofParameterEstimatesParameterMUMAI,1MUMAIJ1.0000.0030.0031.000ToLagChi-SquareDFPr>d•c—A..上__—I.-12Ul11Huiuuur【bdi64.6950.45520.0940.156-0.0220.1150.050127.25110.77850.053-0.132-0.037-0.046-0.026189.33170.92940.023-0.0490.048-0.112-0.0442410.6?230.98830.088-0.030-0.0710.013-0.023AutocorrelationCheckofResiduals0.1510.0580.070-0.00?ModeIforvariable5536.651Estimated5536.651Period(s)ofDifferencingSAS系统2014^05月叩日星期三下午11时03分57秒6TheARINAProcedureMovingAverageFactorsFactor1:1+Q.48349ForecastsforvariablexObsForecastStdError嘛ConfidenceLimits61337276.98377464.6361322646.565?351907.401762342813.633613354.667316638.9869368988.300463348350.283617348.587314347.6774382352.8888B4353886.933620581.541313547.8548394226.012365359423.583523371.482313616.3208405230.8463通过原始数据的时序图可以明显看出，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。从一阶差分后的自相关图可以看出，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：Xt-Xt」=(l+0.48349B)et残差的检验显示，残差序列通过白噪声检验，参数显著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2009〜2013年铁路货运量的预测结果如下：铁路货运与测量2009337276.98372010342813.63362011348350.28362012353886.93362013359423.5835第三题;datayx_53;inputx@@;difx=dif(difl2(x));t=intnx(Tmonth1,f01janl973Tdf;formattdate.;cards;9007.008106.008928.009137.0010017.0010826.0011317.0010744.009713.009938.009161.008927.007750.006981.008038.008422.008714.009512.0010120.009823.008743.009129.008710.008680.008162.007306.008124.007870.009387.009556.0010053.009620.008285.008433.008160.008034.007717.007461.007776.007925.008634.008945.0010078.009179.008037.008488.007874.008647.007792.006957.007726.008106.008850.009299.0010625・009302.008314.008850.008265.008796.007836.006892.007791.008129.009115.009434.0010484.009827.009110.009070.008633.009240.00.procgplot;plotx*t=ldifx*t=2;symbollc=coralv=circlei=join;symbol2c=bluev=stari=join;run;procarima;identifyvar=x(1,12);estimatep=lq=(1)(12);run;

一阶12步差分后的时序图:difx200YTTTTTTTYrrTTTTrYrrTTrTTyrrrrrTTp-rTTrrrYrTTTrrrprTTrTTTYrrTTTTrYrrrTTrrYTTrrTTrprTTrrrrYTTTTrrrpTTTTTTTp-rrrTTrYTTrrrTTyrrrTTrrp-mTTrpTTTrTTYO1JAN73O1MAY7301SCP7301JAH7401MAY7401$EP74O1JAN750lHkY7501SCP7501JAH7601IUY760l$£P7601JAN7701WAY77O1$£P7701JJW7801VAY7801SEP7801JAM79院系统TheARIMAProcedureNameofVariable=xTOC\o"1-5"\h\zPeriod(s)ofDifferencing1,12MeanofWorkingSeries28.83051StandardDeviation390.7296NunberofObservations59Observation(s)eliminatedbydifferencing13LagAutocorrelationsLag01152670■54326.5281.00000-.355840如如如如如如QIQIQIQIQIQIQt«|»«|*■•«T*<1*<1*,1*<1*<1*•!,U*U*!•*1**1*.00.1301892-15071.682-.09872・**0.145745314584.5680.09553帆：0.1468744-17177.694-.11252:w02510.041530.149367617420.9080.11411米卅・0.1495627-31164.460-.20413・$$$$0.1510318-1087.513-.007120.155637915277.1750.10007帆：0.15564210-12434.670-.08145:w0.156729II23801.3630.13521卅卅X出・0.15744512■50866.898-.33318QIQIQIQIQIQIQt0.1614951313767.9430.09018.0.1727531417757.6610.11631.米卅・0.173549CovarianceCorrelation-198765432101234567891SidErrormarkstwostandarderrorsCorrel&tionInverseCorrel&tion10.499200■1>iladjOiabiladiH>al>ill•P•T«/p^p«p«T«/p^p«p20.35733.,。■山山皿奥也30.250040BbilBdithah•Tp40.27020.50.240010alteiaei60.17013.■林.70.251640alteiaei80.21621.酬俐.90.10666.・100.13339.110.11439.120.23765.130.06057.»・140.00932..-19876543210123456781PartialAutocorrelations1-0.35584•ifei«>i.2-0.25802HiQ>al>illHi03-0.04965・*.4-0.14001,呻05-0.05222・出.60.094190牌•7-0.13378・出.8-0.14985.呻0Correlation-198765432101234567891SAS系统2014年05月08曰星期四下午040寸13分20秒2TheARIMAProcedurePartialAutocorrelationsParameterMUMAUParameterMUMAUMAMARIJMU1.0000.2880.2200.22?MA1,10.2881.0000.0670.756MA2J0.2200.0671.0000.159AR1,10.2270.7560.1591.000ToChi-AutocorrelationPr>CheckofResidualsLagSquareDFChiSq■--Autocorrelations---62.6830.4435-0.0450.0550.137-0.1230.046129.2590.4146-0.211-0.0970.079-0.043D.1661816.97150.3206-0.0060.160-0.045-0.0860.1522422.34210.3739-0.090Modelfor-0.013-0.071variablex0.0270.190Correlationsof