時(shí)間序列分析第二章-時(shí)間序列的預(yù)處理

應(yīng)用時(shí)間序列分析實(shí)驗(yàn)報(bào)告實(shí)驗(yàn)名稱第二章時(shí)間序列的預(yù)處理、上機(jī)練習(xí)241繪制時(shí)序圖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語(yǔ)句說明：“procgplotdata=example2_1；是告訴系統(tǒng)，下面準(zhǔn)備對(duì)臨時(shí)數(shù)據(jù)集 example2_1數(shù)中的據(jù)繪圖。"plotprice1*time=1price2*time= 2/overlay;”是要求系統(tǒng)要繪制兩條時(shí)序曲線?！皊ymbol1c=blackv=stari=join; ”，symbol語(yǔ)句是專門指令繪制的格式。輸出的時(shí)序圖見下圖:01JILW Q1AUQM 01浴供 fl0CTU4 IIX7M4 UWE* Q1JMW5兩時(shí)間序列重疊顯示時(shí)序圖242平穩(wěn)性與純隨機(jī)性檢驗(yàn)1平穩(wěn)性檢驗(yàn)為了判斷序列是否平穩(wěn)，除了需要考慮時(shí)序圖的性質(zhì)，還需要對(duì)自相關(guān)圖進(jìn)行檢驗(yàn)。 SAS系統(tǒng)ARIMA過程中的IDENTIFY語(yǔ)句可以提供非常醒目的自相關(guān)圖。dataexample22;input__freq@@;year=intnx（'year','1jan1970'd ,n-1）;formatyearyear4.;cards;97154137.7149164157188204179210202218209204211206214217210217219211233316221239215228219239224234227298332245357301389;;procarimadata=example2_2;dentifyvar=freq;run;語(yǔ)句說明：（1）"procarimadata=example2_2; ”是告訴系統(tǒng)，下面要對(duì)臨時(shí)數(shù)據(jù)集 example2_2中的數(shù)據(jù)進(jìn)行arima程序分析。（2） "identifyvar=freq;”是對(duì)指令變量freq的某些重要性質(zhì)進(jìn)行識(shí)別。執(zhí)行本例程序，IDENTIFY語(yǔ)句輸出的描述性信息如下:NatneofIMrle=freqUeanof^logkSeries222.941StandardDeviation56,82834NumberofObservations39這部分給出了分析變量的名稱、序列均值、標(biāo)準(zhǔn)差和觀察值個(gè)數(shù)。identify語(yǔ)句輸出結(jié)果的第二部分分為自相關(guān)圖，本例獲得的樣本自相關(guān)見下圖。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^!+出余腳期!K*卑”常余啊撤*StdError00J60126O.ZDm?0.2472420.2635010.2774460.2G41940.2858830.2C70710?2人01$**markstwostandarderror&序列FREQ樣本自相關(guān)圖其中：Lag 延遲階數(shù)。Covarianee 延遲階數(shù)給定后的自協(xié)方差函數(shù)。Correlation-----自相關(guān)系數(shù)的標(biāo)準(zhǔn)差?！币灰?倍標(biāo)準(zhǔn)差范圍。2、純隨機(jī)性檢驗(yàn)為了判斷序列是否有分析價(jià)值，我們必須對(duì)序列進(jìn)行純隨機(jī)性檢驗(yàn)，即白噪聲檢驗(yàn)。在 identify輸出結(jié)果的最后一部分信息就是白噪聲檢驗(yàn)結(jié)果。本例中白噪聲檢驗(yàn)輸出結(jié)果如下：AirtocorrElrCfeeckforfhft#NoiseToChi-Pr> LMSquartOFChfSq ~- --"^QtR——1647.61e<J001 0.578 5.5990.402 0.3S4 0.272 0J36其中：ToLag 延遲階數(shù)。檢驗(yàn)結(jié)果顯示，在6階延遲下LB檢驗(yàn)統(tǒng)計(jì)量的P值非常?。ǎ?.0001），所以我們可以以很大的把握（置信水平＞99.999%）斷定該序列屬于非白噪聲序列。、課后習(xí)題2.1975-1980年夏威夷島莫那羅亞火山（ Maunaloa）每月釋放的co2數(shù)據(jù)如下（單位：ppm）,見表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)繪制序列時(shí)序圖，并判斷該系列是否平穩(wěn)。實(shí)驗(yàn)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;實(shí)驗(yàn)結(jié)果:338二C EHJUL750HJAN7E0IJW_76QIJAN77ttlJlJL?338二C EHJUL750HJAN7E0IJW_76QIJAN77ttlJlJL?7CIJAN7801JUL7BD1JAH7901JULTS01J^N80JIJLJL8O Q：IM陶I11lie實(shí)驗(yàn)分析體會(huì)：時(shí)序圖給我們的提供的信息非常明確，夏威夷島莫那羅亞火山（Maunaloa）每月釋放的co2時(shí)間序列圖有明顯的遞增趨勢(shì)，所以它不是平穩(wěn)序列。實(shí)驗(yàn)分析體會(huì)：時(shí)序圖給我們的提供的信息非常明確，夏威夷島莫那羅亞火山（Maunaloa）每月釋放的co2時(shí)間序列圖有明顯的遞增趨勢(shì)，所以它不是平穩(wěn)序列。（2）計(jì)算該序列的樣本自相關(guān)系數(shù) 氏（k=1,2,川，24）實(shí)驗(yàn)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;"|實(shí)驗(yàn)結(jié)果： Correlation0.907510.721710.512520.349820.24690.203090.210210.264290.364330.484720.58456procarimadata=example21;identifyvar=ppm;|run;"|實(shí)驗(yàn)結(jié)果： Correlation0.907510.721710.512520.349820.24690.203090.210210.264290.364330.484720.584560.601980.518410.368560.206710.081380.00135-0.03248(3)繪制該樣本自相關(guān)圖，并解釋該圖形。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自相關(guān)圖顯示序列子相關(guān)系數(shù)長(zhǎng)期位于零軸的一邊，這是具有單調(diào)趨勢(shì)序列的典型特征，同時(shí)自相關(guān)圖呈現(xiàn)出明顯的正弦波動(dòng)規(guī)律，這是具有周期變化規(guī)律的非平穩(wěn)序列的典型特征。自相關(guān)圖顯示出來的這兩個(gè)性質(zhì)和該序列時(shí)序圖顯示的帶長(zhǎng)期遞增趨勢(shì)的周期性質(zhì)是非常吻合的。3.1945-1950年費(fèi)城月度降雨量數(shù)據(jù)如下（單位：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實(shí)驗(yàn)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;自相關(guān)圖：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)計(jì)算該序列的樣本自相關(guān)系數(shù) Pk(k=12川,24)從上面的自相關(guān)圖可以看出樣本的自相關(guān)系數(shù)為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)判斷該序列的平穩(wěn)性。如下圖是該序列的時(shí)序圖:「丁 T 「丁 T 丁 丁 丁 丁01JAMS0UUL45QiJAMBDIJUL45U1J坤47(HJUU70IJ/14BU1JUL48U1JAN套(]1JUL49O1JAM5001JUL5Q0UAN51ti腿根據(jù)序列圖可以知道，圖上可以看出該序列在一個(gè)常值附近上下波動(dòng)，且不具有周期性，判斷該序列為平穩(wěn)序列。(3)判斷該序列的純隨機(jī)性。本序列的檢驗(yàn)結(jié)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因而可以認(rèn)為費(fèi)城月度由于P值顯著大于顯著性水平0.05,所以該序列不能拒絕純隨機(jī)的原假設(shè)。降雨量的變動(dòng)屬于純隨機(jī)波動(dòng)。

因而可以認(rèn)為費(fèi)城月度5.表2-9數(shù)據(jù)是某公司在2000-2003年期間每月的銷售量。銷售量2000年2001年2002<2003年1月1531341451173月18717520317813月23424315$14P■歸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)繪制該序列時(shí)序圖及樣本自相關(guān)圖。實(shí)驗(yàn)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;時(shí)序圖時(shí)序圖自相關(guān)圖:LasCovarianceCorreiationAutccorrelationsdUiLMLMJwLKLi*LMLBJHL自相關(guān)圖: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