sas时间序列课后作业相关系数

1、第二章习题第一题代码如下data example2;in putfreq;time=intnx( year ，1,_n_-1);format year year4; |cards ;1 2 3 4 5 6 7 8 9 10 11 12 13 1415 16 17 18 19 20 proc gplot data =example2;plot freq*time;symbol c=black v=star i =join;run ;结果如下平稳序列的时序图应该显示该序列始终在一个常数值附近波动，而且波动范围有界的特点。 可是上述时序图是一次函数递增趋势的，所以该序列是非平稳序列。uU li丘i

2、I导g朮耳m p ； 卯皆出胃中矽gAS 累统ThursdayasyuptotIc approx Inal Ioused for correThe ARILiA Procedurelie of NLAC is lar&er than 25X of the 淀i ies lerth. The ics anti conf Iderwe interveils miy bt poor.Naims of Variable = f reqMen of fforkinr Series10*5Standard Deviation5.766261Number of Obscrvat ions20Antocarr

3、e I at i on?Std Error033.2500001.00000diiU-diiU-diiL JiiLHjill-iJiHiqfjHidjdi Jadi 斤|1,心|11八1112TuT|t1MTHTMTHTi|Tn 1 nT*128.2625000.85000山Ur山山*山边山*山l| 111 l| 11 p !| 1 IfTll|lTll|lTll|l!Tll|ll ；223.3250000.70150JI I Lrill L1j lIj nj J |_Li J a tfjrpr|Btii ll if ll ip T1 T lip318.4875000*55602桝册附榊柑榊.

4、418.8000000.41504附常附瀬出榊HtB09.312G000.28008附岸出壯弗常.65.0750000.1626811.1375000.084218-2.460000-.07386Hi9-5.637500-.1695610-8.876000-,2518811-10.61250C-,31917聃串當串|E：12-12.300000-,36992-H家串當串|E串13-13.367500-,4026314-13.825000-.4157915-13.56250C-.40708*:*#*#*La Covari anceCorral ati on/ fiirks two standft

5、rd errors0.2236070,3496490.4140700.4498620.4686170.4769130.4793490.4794710.4800370,4830220.4895450,4993420.5133430.52630?0.545000从图中我们发现序列的自相关系数递减到零的速度相当缓慢，在很长的时间延迟时期里， 自相关系数一直为正，而后又一直为负，在子相关图上显示出明显的三角对称性，这是具 有单调趋势的非平稳序列的一种典型自相关图形式，这和该序列时序图的单调递增是一致 的。各个延迟阶数下的自相关系数如下K=1 =0.85K=2? =0.7015K=3 =0.55602K

6、=4? =0.41504K=5=0.28008K=6? =0.152635SPSSFile Edit也 ewQata IransformB LI旦1: fre1(revar11.0022.0033.00A4,0055.006S.OO77.00a3.0099.001010.001111.001212.001313.0014H.OO151500161S.OO1717001819001919.002020. DOReportsBSGrp1jB 宝血iiwTablesCornparB Meansfijerieral Lin刚 ModeiiorrelalfiRegressionLoglinsarNeur

7、al Networksdassiiy却牟 ReductionScaleypnparameiric TeslsTpw SeriesIMutiple RespcriEaComplBX SemplesS aUntitl.Al DtSBiD - POueHy Control0 RCCC.SurviveValue Arasis.L t DInaiye Graphs Utillies Acid-Qns Window HelpModels辰r1 resie Mocfs. 芮1 Affily Models.Generahzed Linear iMjoctefcSeasorialDewnnposition.Sp

8、ectral Anialysis.Series:freAutocorrelationsLagAutocorrelationStd. ErroraBox-Ljung StatisticValuedfo. bSig.1.850.20816.7321.0002.702.20228.7612.0003.556.19736.7623.0004.415.19141.5004.0005.280.18543.8005.0006.153.17844.5336.0007.034.17244.5727.0008-.074.16544.7718.0009-.170.15845.9219.00010-.252.1514

9、8.71310.00011-.319.14353.69311.00012-.370.13561.22012.00013-.403.12671.40913.00014-.416.11784.08714.00015|-.408 |.107 |98.729 15 .000a. The underlying process assumed is independence (white noise).b. Based on the asymptotic chi-square approximation.fre10- CaefficierrtUpper tonfklgnue Limit Lower Con

10、fidence Limit05-y ooa-0 5-10-tiiiitriii i ( i r1234567e910 1112 13 14 15Lg Number第二题代码如下data example2;in putppm;time=intnx(month, 01jan1975d,_n_- 1);format time monyy.;cards ;330.45 330.97 331.64 332.87 333.61 333.55 331.90 330.05 328.58 328.31 329.41 330.63331.63 332.46 333.36 334.45 334.82 334.323

11、33.05 330.87 329.24 328.87 330.18 331.50332.81 333.23 334.55 335.82 336.44 335.99334.65 332.41 331.32 330.73 332.05 333.53334.66 335.07 336.33 337.39 337.65 337.57336.25 334.39 332.44 332.25 333.59 334.76335.89 336.44 337.63 338.54 339.06 338.95337.41 335.71 333.68 333.69 335.05 336.53337.81 338.16

12、339.88 340.57 341.19 340.87339.25 337.19 335.49 336.63 337.74 338.36 proc gplot data =example2;plot ppm*time;symbol c=black v=star i =join;run结果如下平稳序列的时序图应该显示该序列始终在一个常数值附近波动，而且波动范围有界的特点。 可是上述时序图显示每月释放的co2数据以年为周期呈现出规则的周期性，除此之外还有明显的逐年递增的趋势。显然该序列也一定不是平稳序列。绘制样本自相关图代码如下data example2_2;in putppm;time=intn

13、x(month, 1jan1975d,_n_- 1);format time monyy.;cards ;330.45 330.97 331.64 332.87 333.61 333.55331.90 330.05 328.58 328.31 329.41 330.63331.63 332.46 333.36 334.45 334.82 334.32333.05 330.87 329.24 328.87 330.18 331.50332.81 333.23 334.55 335.82 336.44 335.99334.65 332.41 331.32 330.73 332.05 333.533

14、34.66 335.07 336.33 337.39 337.65 337.57336.25 334.39 332.44 332.25 333.59 334.76335.89 336.44 337.63 338.54 339.06 338.95337.41 335.71 333.68 333.69 335.05 336.53337.81 338.16 339.88 340.57 341.19 340.87339.25 337.19 335.49 336.63 337.74 338.36Jproc arima data =example2_2;identifyvar =ppm nlag =24

15、;run ;Name of Variable = ppmi3- .crk ins -?eries 334.5044Standard De?Ietion3,151627Number of Observat ians72AntocorrelatIonsLag Ccvari anceCorrelat i onStd Error2345678901234567890123409.33275219.Q14C507.1S86045.090713.4747002.4623612.0172852.0S79442.S251089.G188214.6145715.S0G3065.9793085.1492643.6

16、608442.0582200.3033340,013455 -OJ22S07 -0.2691B70.1116040.82191G1.Sm322.41E8312.5082481,000000,907510,721710.512520.349820.246900.203090.210210.2S4290,384380,434720.5845S0.B01380.51S410.36S560.208710,081380.00135 -,03248,027100.011240+092750.170110.243200.252521 山 lLf山 il1 山 山1Qnb Jj il*11厂序那-那邓碍中 尊

17、衝CLH15炉和可町那d準if1T11 i|i ip i|i 1111 j 1111T111 j 11111111 |i 111 yn 1iiUj lLp li-i T T* 6应L Jj Jj 山山if -ip rpiniif |-ip1 丄”A 山 山 a，山1 *X* i| ii | |i i|i i|iT1 lTlb if nfjipi 1屮山 7Mb* 1illip m rri. rp jTi ap rfi卅！KHfiH. *跡融,ipii|-ipT1-1937654321012345676910DJ1P851 0.191744 0.226350 0.241932 0.243556

18、0.252237 0.254498 0.256898 a.?60647 0.267627 0*279554 0.296045 0.812584 0.324305 0.330072 0.331865 0.332142 0.332142 Q.382W6 0.882217 0.332222 0.882508 0.333715 0.886167 marks tword errors从图中我们发现自相关系数长期位于零轴一边，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， 这和该序列时序图的带长期递增趋势的周期性质非常吻合。各个延迟阶数

19、下的自相关系数如下：就是上图中第三列correlation的值K=1；? =0.90751K=2? =0.72171K=3? =0.51252K=4=0.34982K=5 =0.24690K=6=0.20309后面的图中有显示所以省略。SPSSAutocorrelationsSeries:PPMLagAutocorrelationStd. ErroraBox-Ljung StatisticValuedfo. bSig.1.908.11561.8031.0002.722.115101.4482.0003.513.114121.7313.0004.350.113131.3204.0005.247.

20、112136.1675.0006.203.111139.4976.0007.210.110143.1197.0008.264.110148.9348.0009.364.109160.1609.00010.485.108180.35010.00011.585.107210.19711.00012.602.106242.37612.00013.518.105266.64613.00014.369.104279.12414.00015.207.103283.11815.000a. The underlying process assumed is independence (white noise)

21、.b. Based on the asymptotic chi-square approximation.PPMU_1234567 S 910 1112 13 14 15 CoeffldertUpper ConfitJenc总 Limit Lower Confidence LimitLag Number第二题代码如下data example2;in putmm;time=intnx(month, 01jan1945d,_n_- 1);format timemony y7.;cards ;69.380.040.974.984.6101.1225.095.3100.648.3144.528.338

22、.452.368.637.1148.6218.7131.6112.881.831.047.570.196.861.555.6171.7220.5119.463.2181.673.964.8166.948.0137.780.5105.289.9174.8124.086.4136.931.535.3112.3 43.0160.897.080.562.5158.27.6165.9106.792.263.226.277.052.3 105.4144.349.5116.154.1148.6159.385.367.3112.859.4Jproc gplot data =example2;plot mm*t

23、ime;symbol c=black v=star i =join;run ;结果如下mm300200100JAN1945JUL1945JAN1946JUL1946JAN1947JUL1947JAN1948JUL1948JAN1949JUL1949JAN1950JUL1950JAN1951time平稳序列的时序图应该显示该序列始终在一个常数值附近波动，而且波动范围有界的特点。可是上述时序图显示每月的降雨量数据大致在一个常数波动，可以主观的认为大致趋于平稳。绘制样本自相关图代码如下data example2_2;in putmm;time=intnx(month , 1jan1945d,_n_-

24、 1);format time mony y7.;cards ;69.3 80.040.974.984.6101.1225.095.3100.648.3144.528.338.447.552.370.168.637.1148.6218.7131.6112.881.831.096.861.555.6171.7220.5119.463.2181.673.964.8166.948.0137.780.5105.289.9174.8124.086.4136.931.535.3112.343.0160.897.080.562.5158.27.6165.9106.792.263.226.277.052.31

25、05.4144.349.5116.154.1148.6159.385.367.3112.859.4proc arima data =example2_2; identifyvar =mm nlag =24 ;95.3458349.5B06472run ; |hfesn of Iorkirif Ser i cs Standard Devi at ion Mumber of Observat iorsLae Govftr ianteCorreia titwi 1Autcccrreleit ions02456.24731,366B0C102.151 -106.195 -438,914 -G17.2B

26、2 -230.421 -166.479-176.79734.00B1762S0.897583.73012 5 用 6113 -61.538174m185.ooe15 -34E.fi3916 -500.06C17 -602.S951$163.24719 -342.53420 -$3,507721 506.307锂-24.23335023137.26514 283.9751.000000.012770.04160-.04323-.25130-.09581-.0B77B-.Q713S0.103450.217300.31587 -.02606 0.07532*.14121-20359*.!454S0J

27、SB46-.13945-.：I34O0.20572-.00387Q.080310.11406T ! |n| |n| *T“r T* sT* T1 T bit*00.117851蛊*0.1178700.1190740.1192940.1219850.128976 *0.129319 #1304100.130360i0.130881iWM,0.182245i*榊*啊0.137114用0.148373D.1469330.147403D.143884QJ53141QJ585120.158889, $：O.1GO6S0啊啊0.1606301-0.1643070.164816OJ648GOStd Erro

28、rmarks two standeird errors从图中我们发现自相关系数大致在0轴附近波动，所以可以主观的认为它是平稳的，各个延迟阶数下的自相关系数如下：就是上图中第三列correlation的值K=1?=0. 01277K=2? =0.04160K=3 =-0.04323K=4=-0.17869后面的图中有显示所以省略。Autoccrrelation Check for White I4oiseToLasChi-SqjareDFPr i Chi Eq&8.5260.2028Q.0130,042-0.D43-0,178-0.251-0.0341223.36120,0248-0,168-0

29、,0720.0140,1090.21701,316IB36.02190.0070-0.0250.075-0.141-0.204-0.245Oi.OCE2444.77240.00620J39-0.034(L2朋-0.010o.oeoo.ne数据个数是72，他的四分之一是 18,所以观察前三行的 p值，由纯随机检验图可以看出, 在延迟阶数为6时，p值大于0.05，是纯随机的，则该规律的波动没有任何统计规律可行。而12、18阶的p值则小于0.05，拒绝原假设，所以认为月度降雨量不属于纯随机波动，说 明该序列不仅可以认为是平稳的，而且还蕴含着值得提取的信息。第四题用exceI计算LB统计量尸0.95（

30、6）=1.635尤：.9（12） 5. 226国文件輪辑視團辺插入格式辺工具泊帀日山壽丨曲丨直丨总（a“町“包无-ziE17 AABCD10. 020. 00044. 0404E-0620. 05a 00252. 55102E-0530.10.010. 0001030934-0. 020. 00044.16667E-0650. 050. 00252. 63158E-0560. 010. 00011.06383E-0670. 120. 0144CL 000154839S-0. 06CL 00363. 91304E-051. 674735g0. 08a 00647. 0329馆-0510-Q 05

31、0, 00252. 77778E-05it0. 020. 00044. 49438E-0612-0. 050. 00252. 84091E-05134. 989531所以根据自己的计算结果：当延迟阶数为6阶时，大于1.635,所以拒绝原假设，认为是非纯随机的，所以该序列是有 价值的。当延迟阶数为12阶时，小于5.226,所以接收原假设，认为是纯随机的，所以该序列再延 迟阶数为12时是没有价值的。第五题代码如下data example2;in putsale;n_- 1);time=intnx( month , 01jan2000d format time mony y7.;cards ;153

32、13414511718717520317823424318914921222721417830029829524822125622020220123723116217516517413512312411912010410685968587679078747563proc gplot data =example2;plot sale*time;symbol c=black v =star i =join;run结果如下JAN2000APR2000JUL2000 OCT2000JAN2001APR2001JUL2001 OCT2001JAN2002 APR2002JUL2002 OCT2002JA

33、N2003APR2003JUL2003 OCT2003JAN2004 time该时序图显示某公司销售量在后期有明显的递减趋势，是非平稳序列绘制样本自相关图代码如下data example2_2;in putsale;n_- 1);time=intnx( month , 1jan2000d format time mony y7.;cards ;1531341451171871752031782342431891492122272141783002982952482212562202022012372311621751651741351231241191201041068596858767907

34、8747563proc arima data =example2_2; identifyvar =sale nlag =24 ;runDeviation64,82357Number of ObservationsSid Error04202.373LO0000jiiliiiljdf lirdrdinii-JiiijiiliiljdfilBdrdifJididiiai ii ii iy rfi 171 T* T11T1 uH1 T1 T1 T11T11 13548.5140.84431Ji1111HiLjiK11 a Ul1-|Jj*j1jiLlll|LrlU-Uj23158.S340.7515

35、4lLh iJjiJj iJj L* hJj dV Jj Jj Qj lLp lLi4 邛i|iifiiy*!沪rp qi平-qilyiiTnri*T, Prp32924.2880.6S577lli.JjI Ii IIiilitil ir l ii liilnriilai !42818.4S80.694405Z47B.3160.58920LiliJiliudfdfdi-iildlsJlUililiihi i11| JIp11|ii1111.E1929,7380.459151 jl 11H 1 1 llji 11 111 宙也出辞MR审不11647.8020.49S53 ll ill |T 1i

36、h mm幅用eem中m.81644.907Q.43896l91545.2080.3S7BB出眾*1|1圖：+101020.1680.244639fJjLgjiiuilrdf11582.850O.138SS12449.1880.10688出1*+Autocorrelat i onsLag Covariance Correlat ion -1 9376543?1 0 1 2345678S 1/ tfirks to standard errors0.14483S0.2248010.2721670.30B98G0,3381290.35S8S20.3709180.3816140.3919930.3931

37、120.402224C.403?19自相关图显示自相关系数一直为正，而且有递减趋势，所以是非平稳序列。Li&12Squart148,41188.39DFE12ChiSqAutocorrelat ions-D.4690.10?.0001ChiSqhU I cor re 1 al 1 oriS 664.0?EC00010.50K0.539D.87J0.2910.25S0.1481288.9812.0001D.2700.188D,1780.2580.2070.226对数据进行函数y厂xt-xz运算后的结果如下代码如下data example2; |in putfreq;time=i ntnx( 28

38、 ，O1ja n1969d,_n_- 1);format timemonyy7.;cards ;5-502-2-303 4-69-3 4-1562-1-462-415 440-217-330-722-1921-7-3-5-42-674-12-68-86-326-5-46 0 -2-732-713-80-15-6 4-22-5 proc gplot data =example2;plot freq*time;symbol c=black v=star i =joi n; run ;结果如下frag-30JUL19CB JANI9B9 JUL19B9 JAN1370 JUL 1370 JAN197

39、I JUL1971 JMl97f JUL1972 JANI973 J11L19 苗 JAN1974t m30-10；-20 ；20由时序图可知该序列大致在零左右波动，基本稳定，为了稳妥，继续进行自相 关图检验，初步可以认为平稳序列。绘制样本自相关图代码如下data example2_2;in put freq;time=intnx( 28, 1jan1969d,_n_- 1);format timemonyy7.;cards ;5-502-2-3034-69-34-156 2-1-462-415 440-217-330-722-1921-7-3-5-42-67 4-12-68-86-32 6-

40、5-460-2-73 2-713-80-15-64-22-55proc arimadata =example2_2;iden tifyvar =freq ;run ;Name of Vari able = freqMean of Work I re Series -0,07246Standard Deviatian7.42561Number of Observat ions69Autocar re I at iQ-12345 6789Q123456755.1396771.00000-29.193783-.6294510.7513710.10498-4.435011-.08043-3,267475-.059285.08