时间序列分析第二章-时间序列的预处理

应用时间序列分析实验报告实验名称第二章时间序列的预处理、上机练习241绘制时序图dataexample21;input pricelprice2;time=intnx('month'~~:―‘ijul2004'd ,n-1);formattimedate.;cards12.8515.2113.2914.2312.4114.6915.2113.2714.2316.7513.5615.33procgplotdata=example2_1;plotprice1*time=1price2*time=2/overlaysymbol1 c=blackv=star i=join;symbol2 c=red v=circle i=spline;run语句说明：“procgplotdata=example2_1；是告诉系统，下面准备对临时数据集 example2_1数中的据绘图。"plotprice1*time=1price2*time= 2/overlay;”是要求系统要绘制两条时序曲线。“symbol1c=blackv=stari=join; ”，symbol语句是专门指令绘制的格式。输出的时序图见下图:01JILW Q1AUQM 01浴供 fl0CTU4 IIX7M4 UWE* Q1JMW5两时间序列重叠显示时序图242平稳性与纯随机性检验1平稳性检验为了判断序列是否平稳，除了需要考虑时序图的性质，还需要对自相关图进行检验。 SAS系统ARIMA过程中的IDENTIFY语句可以提供非常醒目的自相关图。dataexample22;input__freq@@;year=intnx（'year','1jan1970'd ,n-1）;formatyearyear4.;cards;97154137.7149164157188204179210202218209204211206214217210217219211233316221239215228219239224234227298332245357301389;;procarimadata=example2_2;dentifyvar=freq;run;语句说明：（1）"procarimadata=example2_2; ”是告诉系统，下面要对临时数据集 example2_2中的数据进行arima程序分析。（2） "identifyvar=freq;”是对指令变量freq的某些重要性质进行识别。执行本例程序，IDENTIFY语句输出的描述性信息如下:NatneofIMrle=freqUeanof^logkSeries222.941StandardDeviation56,82834NumberofObservations39这部分给出了分析变量的名称、序列均值、标准差和观察值个数。identify语句输出结果的第二部分分为自相关图，本例获得的样本自相关见下图。AutxorrelationsCorrectIon7卜"i 「一"3229.4801865.2671933.3971299.5361238.607877.946CorrectIon7卜"i 「一"3229.4801865.2671933.3971299.5361238.607877.946439.920375.21533L853292.3841JOOOO

0.57758

0.59S67

0.W400J93530.2718B0.1962)0.116190J0276OJ9054|ii11d|^nnn|.rdi-JJLiJilfHidiAIiijjiL-di-diidiiLFbididcijjdi-JiilJiL-iliiJiiriiilfiHi-iTiqiiiprpiiTiiTirrAi|iJiuiip>>1"ii|i|"|i ;iiii|i|iIjhdrillfdiiiuiLrill.diJJiUiL-iiinin|ii|ir|ii|7iITipjTtrTT出余制^!+出余脚期!K*卑”常余啊撤*StdError00J60126O.ZDm?0.2472420.2635010.2774460.2G41940.2858830.2C70710・2人01$**markstwostandarderror&序列FREQ样本自相关图其中：Lag 延迟阶数。Covarianee 延迟阶数给定后的自协方差函数。Correlation-----自相关系数的标准差。”一一2倍标准差范围。2、纯随机性检验为了判断序列是否有分析价值，我们必须对序列进行纯随机性检验，即白噪声检验。在 identify输出结果的最后一部分信息就是白噪声检验结果。本例中白噪声检验输出结果如下：AirtocorrElrCfeeckforfhft#NoiseToChi-Pr> LMSquartOFChfSq ~- --"^QtR——1647.61e<J001 0.578 5.5990.402 0.3S4 0.272 0J36其中：ToLag 延迟阶数。检验结果显示，在6阶延迟下LB检验统计量的P值非常小（＜0.0001），所以我们可以以很大的把握（置信水平＞99.999%）断定该序列属于非白噪声序列。、课后习题2.1975-1980年夏威夷岛莫那罗亚火山（ Maunaloa）每月释放的co2数据如下（单位：ppm）,见表2-7.

330.45330.97331.64332.87333.61333.55331.9330.05328.58328.31329.41330.63331.63332.46333.36334.45334.82334.32333.05330.87329.24328.87330.18331.5332.81333.23334.55335.82336.44335.99334.65332.41331.32330.73332.05333.53334.66335.07336.33337.39337.65337.57336.25334.39332.44332.25333.59334.76335.89336.44337.63338.54339.06338.95337.41335.71333.68333.69335.05336.53337.81338.16339.88340.57341.19340.87339.25337.19335.49336.63337.74338.36(1)绘制序列时序图，并判断该系列是否平稳。实验程序:dataexample21;inputppm@@;time=intnx('month','01jan1975'd ,_n_-1);formattimedate.;gards; 330.45330.97331.64332.87333.61333.55331.90330.05328.58328.31329.41330.63331.63332.46333.36334.45334.82334.32333.05330.87329.24328.87330.18331.50332.81333.23334.55335.82336.44335.99334.65332.41331.32330.73332.05333.53334.66335.07336.33337.39337.65337.57336.25334.39332.44332.25333.59334.76335.89336.44337.63338.54339.06338.95337.41335.71333.68333.69335.05336.53337.81 338.16 339.88 340.57 341.19 340.87339.25 337.19 335.49 336.63 337.74 338.365procgplotdata=example2_1;plotppm*time=1;symbol1c=blackv=stari=join;run;实验结果:338二C EHJUL750HJAN7E0IJW_76QIJAN77ttlJlJL?338二C EHJUL750HJAN7E0IJW_76QIJAN77ttlJlJL?7CIJAN7801JUL7BD1JAH7901JULTS01J^N80JIJLJL8O Q：IM陶I11lie实验分析体会：时序图给我们的提供的信息非常明确，夏威夷岛莫那罗亚火山（Maunaloa）每月释放的co2时间序列图有明显的递增趋势，所以它不是平稳序列。实验分析体会：时序图给我们的提供的信息非常明确，夏威夷岛莫那罗亚火山（Maunaloa）每月释放的co2时间序列图有明显的递增趋势，所以它不是平稳序列。（2）计算该序列的样本自相关系数 氏（k=1,2,川，24）实验程序:dataexample21;inputppm@@;time=intnx（'month','01jan1975'd ,n-1）;cards330.45330.97 331.64 332.87333.61333.55331.90330.05 328.58 328.31329.41330.63331.63332.46 333.36 334.45334.82334.32333.05330.87 329.24 328.87330.18331.50332.81333.23334.55335.82336.44335.99334.65332.41331.32330.73332.05333.53334.66335.07336.33337.39337.65337.57336.25334.39332.44332.25333.59334.76335.89336.44 337.63 338.54339.06338.95337.41335.71 333.68 333.69335.05336.53337.81338.16339.88340.57341.19340.87339.25337.19335.49336.63337.74338.36formattimedate.;5procarimadata=example21;identifyvar=ppm;|run;"|实验结果： Correlation0.907510.721710.512520.349820.24690.203090.210210.264290.364330.484720.58456procarimadata=example21;identifyvar=ppm;|run;"|实验结果： Correlation0.907510.721710.512520.349820.24690.203090.210210.264290.364330.484720.584560.601980.518410.368560.206710.081380.00135-0.03248(3)绘制该样本自相关图，并解释该图形。AutocorreltonsLagCovarianceC中flatIon-1M7643211045671MStdError0123457E310II1213149.8327529.0140507,1686045.0S07163.4747002.4523S12.017285Z.0B79442.25106焉IE17ie4.B145716.BD63DG5.97330S5.1492643.E60S442.053220O.BOBS840.013455-0.8226071.000000.907510.7?171D.512520.349B20.246900.203090.210210.264290.364330.4S4720.584560.G01880.51S410.3G85B0.206710.0S1380.00135-.03248lUiUiUiUiUiUihijuduiLiilLiihjikiiLiiLiikiikiiiBTiHpiipupiiriirigifr.nBh，工rTT工TTiM[U知11j1iUi1f>LiiJijikiikJiJuijLiikJikiifaii£iipiHpupiirnrn|iiHi|uiiLaiLaiUiUiUiUi"iiuiiiiiiLiikiikiipiifeiiiiipiifiifiifiipiipupup>>T'T・T*****,****.00.1170510J917440.2288500.2419320.2460580.2522370.2544980.25B8880.2606470.2B7B270.2795540.29B0450.3126840.8243050.3300720.3318650.3321420.332142〃.diarkstwostandarderrors自相关图显示序列子相关系数长期位于零轴的一边，这是具有单调趋势序列的典型特征，同时自相关图呈现出明显的正弦波动规律，这是具有周期变化规律的非平稳序列的典型特征。自相关图显示出来的这两个性质和该序列时序图显示的带长期递增趋势的周期性质是非常吻合的。3.1945-1950年费城月度降雨量数据如下（单位：mm69.38040.Q.74JS4.6101.1225Q5.3100.64S.3144.328.338452.36S637114S.6218.7131.(5112.8Sl.S3147.570.196.86L?55.fi171.7220.5119.463.2181.664.8166.9137.7SOS105.2899174.812486.4136.93L535J1123160.89780.562.515S.27.61C5.9106792.263.226J7752.3105.4144.349.5116.154,114&.6159.385.367.3112.S的.4实验程序：dataexample2_3;inputfreq@@;time=intnx('month','1jan1945'd ,n-1);formattimedate.;cards;80.040.974.984.6101.1225.095.3100.648.3144.5128.352.368.637.1148.6218.7131.6112.881.831.047.570.196.861.555.6171.7220.5119.463.2181.673.964.8166.948.080.5105.289.9174.8124.086.4136.931.535.3112.3143.097.080.562.5158.27.6165.9106.792.263.226.277.052.3114.349.5116.154.1148.6159.385.367.3112.859.4;;procarimadata=example23;identifyvar=freq;run;自相关图：AutocorrelatiotnsLagCovarianceCorrelation-1SidError12345678311J36S.51I142.228-102.461-230.974-311.479-135.70873.042640-214,021r5.49232658.S86648402.430650J39LagCovarianceCorrelation-1SidError12345678311J36S.51I142.228-102.461-230.974-311.479-135.70873.042640-214,021r5.49232658.S86648402.430650J39-28.71657470.405511-397*E5a<360.919-433,S90191.745LOGOOOOJGOOfi.04826-.09752-.Z1647-.13151[05730C.03337-J02320.025200J68910.27451712120.02973-J6785-.15238-J63190.08098IBiBala■1iiillallalm1■Jiidi *JL*"Jj lr"±.nt**笥帝*出苗水m*HiHiK■lialisLBitiJim*出弗水¥Hi出出水Li0J17810.1182750J184950.119G040J248270*1266350J271840J273160J2B2U4QJ282040,1232730J313620J391010J3911B0,139204fl1419870,1442410.147437twostuidarderrors(1)计算该序列的样本自相关系数 Pk(k=12川,24)从上面的自相关图可以看出样本的自相关系数为Correlation0.06005-0.04326-0.09752-0.21647-0.13151-0.057300.03337-0.09036-0.002320.025200.169910.02973-.16785-.15233-.183190.08096

(2)判断该序列的平稳性。如下图是该序列的时序图:「丁 T 「丁 T 丁 丁 丁 丁01JAMS0UUL45QiJAMBDIJUL45U1J坤47(HJUU70IJ/14BU1JUL48U1JAN套(]1JUL49O1JAM5001JUL5Q0UAN51ti腿根据序列图可以知道，图上可以看出该序列在一个常值附近上下波动，且不具有周期性，判断该序列为平稳序列。(3)判断该序列的纯随机性。本序列的检验结果如下:AutocorrelationfOhMfliiteNoiseToLaeChiSquareDFPr>ChlSqAutocorrelationse札4Ee0.9S0-0.043O.0S8-O,21S•0.182-0,05712IB.5012-0.090-0.Q020J?00.275IS25.3&IS0.1160-0.0120030-0.168-0.152-0.1830.031因而可以认为费城月度由于P值显著大于显著性水平0.05,所以该序列不能拒绝纯随机的原假设。降雨量的变动属于纯随机波动。

因而可以认为费城月度5.表2-9数据是某公司在2000-2003年期间每月的销售量。销售量2000年2001年2002<2003年1月1531341451173月18717520317813月23424315$14P■归212227214178壬月300298295248疔月221256220202了月201237231162&月17516517、|135p月123124120月1Q41068596口月S5£7(579012月787475<53(1)绘制该序列时序图及样本自相关图。实验程序：dataexample23;input__number@@;,n-1);time=intnx('month','1jan2000'dformattimeyymmdd10.;,n-1);cards;153187234212300221201175123104857815318723421230022120117512310485781341752432272982562371651241068774145203189214295220231174119856775117178149178248202162135120969063513417524322729825623716512410687741452031892142952202311741198567751171781491782482021621351209690635procgplotdata=example23;plotnumber*time=1;symbol1c=blackv=stari=join;procarimadata=example23;identifyvar=number;run;时序图时序图自相关图:LasCovarianceCorreiationAutccorrelationsdUiLMLMJwLKLi*LMLBJHL自相关图:LasCovarianceCorreiationAutccorrelationsdUiLMLMJwLKLi*LMLBJHLILIMiAiwLnl>LIHiAi-Jt-J.-■L・>■:■J■平isi!if!riiitnale1aillilla1i1jIB・I11j1lillillillalaill181s11if.rgiiyijyiifAiTryiiprpsifiiTiiyiiy；i|iStdError4202*8781£345g76911123108,0141920.808841.'1345.166-2600.731-3080.1BQ-264J.955-1427.30247.S434241402.5722436.3433071.9Bfl1.000000.739500.457040.081E3