时间序列分析报告

1、时间序列分析报告.模型变量的选择和数据的出处报告内的数据是1978年到2014年的浙江地区生产总值的原始数据。该数据来源于中华人民共和国国家统计局官网：(http:浙江地区生产总值年份1978197919801981198219831984198519861987198819891990199119921993199419951996199719981999200020012002200320042005200620072008200920102011201220132014123.72157.75179.92204.86234.01257.09323.25429.16502.47606.99

2、770.25849.44904.691089.331375.71925.912689.283557.554188.534686.115052.625443.926141.036898.348003.679705.0211648.713417.6815718.4718753.7321462.6922990.3527722.3132318.8534665.3337756.5940153.5.将数据输入SA器序datasasl;inputyearx;cards;1978123.721979157.751980179.921981204.861982234.011983257.091984323.25

3、1985429.161986502.471987606.991988770.251989849.441990904.6919911089.3319921375.719931925.9119942689.2819953557.5519964188.5319974686.1119985052.6219995443.9220006141.0320016898.3420028003.6720039705.02200411648.7200513417.68200615718.47200718753.73200821462.69200922990.35201027722.31201132318.85201

4、234665.33201337756.59201440153.5)run;procprintdata=sas1;run如图所示:Obsyear工119781?3.7221575157.753193017S.S24isai4,加519022U.U161963257.09?323.25819954?3,1691哪592.47101307606.3911侬*770.251?18明S49.4413胸-4*91418911099.381519921375.7016侬31925dl1?19912G39.2S1819953557.551919964l3fi.E32019974636JI2119985052X

5、22219995443.32232000$141郃2420016898.34252002SC03.C7州200S9706.02272UU411648.70282UU513417.6823200616714?30200718753.7331加821462.6332200922990.35S3201027722.3134201192310J535201?346&5J3gu20138775B.5937201440153.SO三.对数据的平稳性和非白噪声性进行检验1 .平稳性检验procgplotdata=sas1;plotx*year;symbolc=bluei=joinv=star;run

6、;如图所示：-T5CCOT：3raHl-X-r二-1CCW-丐他髀M10式布)10102020year由图可知，该组序列呈现的是明显的指数上升趋势，因此要对该组数据进行对数处理。2 .对数据进行对数处理datasasl;|inputx;y=log(x);year=intnx('year','1jan1978'd,_n_-1);formatyearyear4.;cards;123.72157.75179.92204.86234.01257.09323.25429.16502.47606.99770.25849.44904.691089.331375.71925.9

7、12689.283557.554188.534686.115052.625443.926141.036898.348003.679705.0211648.713417.6815718.4718753.7321462.6922990.3527722.3132318.8534665.3337756.5940153.5；run;procprintdata=sas1;run;如图所示:123a.918013761G7.7E5,QE1U1979179.9!54G5.3223Ml234.015.45541332对.仲5.54941岫3328.255.7734w429JB8.0GB

8、1305G.219519鸵6C6.9S6.408519SF770.26G.C4G719鸵849.44S.74461989904.est.SC7C1390108S.3S6.898819SI限.M7,Z2B713921925.917.5C821383280fi.se7.9S701跑3557.553J768133541gB.隔9.3401199646佩118.152419375052.技8.5277跳86448.S28.SC2318396Ml.%8.7227沛QQ6853,848.S38020018003.S78.8B77200297C5.029.IQD4200311643.763.36292004

9、13417.EQ9.5043200515718.479.662608107E9.79B.03912007214?.6S9.874120DB2299O.3E10.042820D9m组8i10.2S00201032318.BE10,9084201134665.3310,45352012377EB.BS10,5339201340153.501D,S0052D1412845-678901-UJ-84567800012_345G789O128458711111111112-2-2222-2222933333333.对数处理之后数据的平稳性检验procgplotdata=sas1;ploty*year;s

10、ymbolc=bluei=joinv=star;run；4 .对数据进行一阶差分datasas1;setsas1;z=dif(y);procgplotdata=sas1;plotz*year;symbolc=bluev=stari=join;run;如图所示:由图可知，该序列进行一次差分处理之后，数据呈现波动趋势，我们粗略的认为该序列处于平稳状态。5 .进行非白噪声检验procarimadata=sas1;dentifyvar=z;run;如图所示:自相关图:riutocorrelationsLeisCovarianceCorrelation0.00531360.002&5760-00

11、062859-0.0002852-0.001G299-0.0017809-0.00053BEC.00034834I.OCOOO。,5圻部0,11830-,04427-JCS74-.32575-JC09B0,0(1192720.0011279U.0E56?0J98320J6872心山山3山*山UrdJl1*diih山山ijiipi|ii|iiir|iiprfir|ii|iriinijTir|ii|i"ll'T'lTl'T"lll*山*山g山*diUrd-idfrlii|i-!i|iirpi|'i|up榔Hi出出由*HiiH*布指itarkstw

12、ostandarderrors并且MR(1)模型，并且由图可知，自相关系数从延迟一阶后就进入了两倍标准差的范围之内,自相关系数衰减速度迅速，是截尾的，由此可判断该序列是是处于平稳状态O逆自相关图和偏自相关图:InverseAutoccrreIatiorsCorrektIqh0.36705-0.S28250.29212-0.032540.01387-0,031$60.00926-0.02873Partial叮TaiTay11T1aip-irTa111IllilillllllHidi«T«T«iT|iJil'lliiIihil*IJ：l|«l|Bfl

13、lTAutoccrrelatiansCorrelation765432101234567891出*出(1吊中*iW11111Iilc11illmHillill；摩胴串即季制币;fh中币m由图可知，偏自相关系数从延迟一阶后就进入了两倍标准差的范围之内，并且偏自相关系数衰减速度迅速，是截尾的，由此可判断该序列是AR(1)模型纯随机性检验结果：AntocdrrelitionCheckforWhitsMoiseIcChi-Pr>LasSquareDFChlSqAjtoccrrelaIans621.也由0.00170-588DJI8-0J044-0.807-0.826-0.101由图可知，在显著性

14、水平0.05下，延迟6阶后的检验P值都比小，因此拒绝原假设Ho,认为序列为非白噪声序列。所以我们认为一阶差分后的时间序列是平稳非白噪声序列。四.ARM模型的识别和定阶1.模型的识别procarimadata=sas1;identifyvar=znlag=12;run;如图所示：自相关图:CovftriinceCorrelMion-I337G54321D123456789100.005819S1.00000>Ji山"曲，厩山J，m和illaj.-J-Hlrf|Hr"|is""1ipinr-Iisit10.00286780.63783»山Ur

15、山山山W；山山*11f*!rjsrp'tifpn|nrprfiFp2O.OOOG2869OJ1S30a-0.00023&2-.044?.布4-0.0016299.30674.Hi*15-0.0017303-.32575.帕格附寄出Bl6-0.0005365-.10096.零出70,00034094O.OftFB?时.80.00102720.19832器厢器.90.0014即80.26872郴愀出*.100.000599590.11期mu*,11-0.000Z74B-.061BO12'0.0003353,07262.用Autocorrelationsmarlestwost

16、andarderrorsSidError0o.ieece70,加93981,2112400.21K040,2235200.£363400.297F350.2880380.2428600.2605000.Z51BB10.252156由图可知，自相关系数在延迟一阶后就全部落入两倍标准差区域以内，并且非零值衰减的过程非常突然，因此我们认为自相关系数截尾，且是MR(1)模型逆自相关图和偏自相关图：LasCarrelation-1307654321()12345e7asi1-0.6158411»1J111ialliiafliifirii'T'iriiT'nii

17、T'ifiirTin'20.8B210.1.lail:jJuli.JaiIi不用S不而尊,不3'O.33E81M.«11ifa111111b中市淮即摩m市0.24647IbJhniallill5'0,07611榔60.09709:1-0,00/40榔80.043$1器3-0.1Q0S8100,04573*.110.03676*12-0,03172*InverseiutocorrelotionsLasCorrelation,1387854321()12SJ58788110,53783山ti山;命山if*鼻/舒小2-0,24053*卡布卡布用i30,009

18、224-0,877681111111111j1111,11illTi.T.bTi：T.iT»150.06573出60,07688林.7O,OS923.M!.80.06438*.90.05224*.10-0,13346*布卡110.01249120.(15837琳.Partialiutacorrelations由图可知，偏自相关系数在延迟一阶后就全部落入两倍标准差以内,并且非零值衰减为小值的过程非常突然，所以我们认为偏自相关系数截尾，且是AR(1)模型纯随机性检验结果:The蝌1网ProcedureAutocorrelationCheckforhiteNoi与白TaChiLei6Squ

19、are621.121?27.30&FChiSq60JD17120.0057Autocorrsktions比前EP.118-0.044-P,307-04326-0.101(LU660.1330.2530.111-0.052-0.073由图可知，在显著性水平0.05下，延迟6阶和延迟12阶后的检验P值都比小，因此拒绝原假设H。，序列为非白噪声序列。所以我们认为该序列是平稳非白噪声序列。2.模型的优化procarimadata=sas1;identifyvar=zminicp=(0:5)q=(0:5);run;如图所示:TheARINAProcedureMinimumImorrwtionCr

20、iterionsMA0MA10-5-3363-5J43071-5,7362S-BJ37312-5.84?25-5.？49493-5.80834-5.710434-6.95112-5,S£E905-6.9G471-5-9C5S8购2UA3-5.69475-5.66778-6.723-5.6626-5.B646-5.79575-5.61033-5.70558-5.82599-5.74071-5.82152-5.72213他4MA5-5.5291GT.B胱61-5.64812-6.82581-5.767G2-5.81023-5.G6808-5.70142-5.6E91G-5.G244E-5

21、.82372-5.52S86Ermrie£madeI:ARCS)MlnllUiTableValue：BIC(Q.O)=-5.96471由图可知，模型优化为ARMA1,5)模型，但该模型与前面通过自相关图和偏自相关图所判断的模型不同，因此比较上图中MR(1)和AR(1)的信息量大小,MR(1)信息量为-5.74307,AR(1)信息量为-5.79628,因此我们最终定为AR(1)模型。所以，我们选择AR(1)模型拟合原序列。五.模型参数的估计procarimadata=sas1;dentifyvar=z;estimatep=1method=ml;run;如图所示:TheARTMfiPr

22、ocedureHsimumLiLeiihoodEstimationParaniBterE$t1mateStandardErrorIValueApproxPr>ItllLasMU幅1,10.160050.571350.023220.148976.S33.57caooi01ConstartEstimateVarianceEstimateStdErrorEatIMiteAICSBCNumberofFesidua1sO.0S880S0.0038+60.062013-85.884-92.521336CorreIation?ofPrarmeterE?timatesParameterMUARUMU1.

23、0010-0.086AR1J-O.08G1.000由图可知，在显著性水平0.05下，所有被估计参数的检验值P值都小于0.05,因此拒绝原假设，认为未知参数显著M*jtocorrelotionCheckofFitsiduaIaTcL蛤ChiSquarePr>ChiSqe10J15塞0-0.1710.110-0.270-0.33?0.0461215.83110,1瞰0苕0.06505刖-fl.127-0.0551618.3317。.瞅4-0.074-0.0780,09?0.125-0.027-0.0D72420.01230.21560.043-0.155-0,233Q.愉0,072-OJOSOFAutcxorrelfttlomModelforvariablleEstimatedHe*n0,160047由图可知，在显著性水平0.05下，延迟6,12,18,24期的检验值P值都大于0.05,所以认为残差序列为白噪声序列，并且模型拟合良好。Autoregressivt?FactorsFactor1：1-0.67183B*