實驗三平穩(wěn)時間序列分析

實驗三平穩(wěn)時間序列分析一、實驗?zāi)康模菏煜A、AR、ARMA模型的樣本自相關(guān)系數(shù)和偏相關(guān)系數(shù)的特點，利用它們識別和建立ARMA模型17.某城市過去63年中每年降雪量數(shù)據(jù)（單位：nun）如表3?20?126.482.478.151.190.976.2104.587.4110.52569.353.539.863.646.772.979.683.680.760.37974.449.654.771.849.1103.951.682.483.677.879.389.685.558120.7110.565.439.940.188.771.48355.989.984.8105.2113.7124.7114.5115.6102.4101.489.871.570.998.355.566.178.4120.597110表3?20（1）判斷該序列的平穩(wěn)性與純隨機性該序列的時序圖如下（圖1）圖1由時序圖顯示過去63年中每年降雪量數(shù)據(jù)［韋|繞早70mm附近隨機波動，沒有明顯趨勢或周期，基本可以看成平穩(wěn)序列，為了穩(wěn)妥起見，做了如卞自相關(guān)圖（圖2）AutocorrelationsStdError0553.6991.00000ibHfihalfihihihiihiliihilfihnfihalfihihilsihili<T*??!*"T* U"H*?T? ??!*"T* U"*!?11G9.516StdError0553.6991.00000ibHfihalfihihihiihiliihilfihnfihalfihihilsihili<T*??!*"T* U"H*?T? ??!*"T* U"*!?11G9.5160.30615?ibHfiholfihih2183.7780.29579?ibHfiholfihih320.8777310.03734*?470.1496060.12669?54.9747980.0089864.6392040.008387-39.057637-.07054?*8-36.488733-.06590?*9-27.507653-.04968?*108.1672380.014751131.4536170.05681出 ?1242.0715910.07598出捲 ?1350.2669040.09078出捲 ?1463.2717710-11427出捲 t1565.5339700-11836出捲 tLagCovarianceCorrelation198765432101234567891markstwostandarderrors00.1259880.1372900.1470580.1472080.1489290.1489380.1489450.1494740.1499350.1501960.1502190.1505600.1511670.1520300.153387圖2自相關(guān)圖顯示該序列自相關(guān)系數(shù)一直都比較小，1階開始控制在2倍的標準差范闈以內(nèi)，可以認為該序列自始自終都在零軸附近波動，這是隨即性非常強的平穩(wěn)時間序列。純隨機性檢驗見下圖：（圖3）AutocorrelationCheckforWhiteMoiseToChi-Pr>LagSquareDFChiSq--Autocorrelations--613.2860.03870.3060.2960.0370.1270.0090.0081214.89120.2474-0.071-0.088-0.0500.0150.Q5?0.076圖36階以內(nèi)P值顯著小于0.05,可以認為這個擬合模型的殘差序列不屬于白躁聲序列（2）如果序列平穩(wěn)且非白躁聲，選折適當模型擬合序列的發(fā)展模型識別如下圖（圖4）TheARIMAProcedureMinimumInforrnationCriterionLagsMA0MA1MA2MA3iMA4MA5AR06.0663776.0112885.9675835.9697615.9937318.028832AR15.9156765.9558785.9916686.0112136.0413396.091295AR25.9263755.9908736.0562016.0649216.0950376.15154AR35.9472066.0129048.0749118.13058.14391?8.188833AR45.9989276.05146.1169688.1766416.2065736.251795AR56.0342446.0865266.144466.2096428.2633448.315751ErrorseriesmodeI: AR(10)MinimumTableValue：BIC(UO)=5.915676圖4最后一條信息顯示，在自相數(shù)遲階數(shù)小于等于5,移動平均延遲階數(shù)也小于等于5的所有ARMA（p.q）模型中，EIC信息量相對最小的是ARNIA（1,0）模型，既AR（1）模型。（3）利用擬合模型，預(yù)測該城市未來5年的降雪量?預(yù)測結(jié)果如下圖（圖5）

S釀系統(tǒng)TheARIMAProcedure2010年門月22日星期一下牛2010年門月22日星期一下牛OB時2ObsForecastStdError95%ConfidenceLimits6490.110422.445948.1173134.10356592.048323.283346.4138137.6828&682.642524.274135.0662130.21896783.899624.275836.3199131.47936881.481224.489833.4620129.4604圖5由圖得未來5（64-68年）90.1nmi^92.0nuii>82.6mm、83.9mm、81.5iniiio18?某地區(qū)連續(xù)74年的谷物產(chǎn)量（單位：千噸）如表3?21所示0.970.451.611.261.371.431.321.230.840.891.181.331.210.980.910.611.230.971.10.740.80.810.80.60.590.630.870.360.810.910.770.960.930.950.650.980.70.861.320.880.680.781.250.791.190.690.920.860.860.850.90.540.321.41.140.690.910.680.570.940.350.390.450.990.840.620.850.730.660.760.630.320.170.46表3?21（1）判斷該序列的平穩(wěn)性與純隨機性該序列的時序圖如下（圖6）圖6由時序圖顯示過去74年中每年谷物產(chǎn)量數(shù)據(jù)|制繞早0.8T?噸附近隨機波動，沒有明顯趨勢或周期，基本可以看成平穩(wěn)序列，為了穩(wěn)妥起見，做了如卞自相關(guān)圖（圖7）

CovarianceCorrelat.ion1987654321()123456789100.0863811.00000CovarianceCorrelat.ion1987654321()123456789100.0863811.0000010.0313930.36342■20.0229940.26613■30.0195790.2266640.0188330.2122450.0163400.1891660.0179160.2074070.0125430.1452080.00314910.0384690.0137670.15937100.0140870.16320110.0106130.12286120.00878840.1017413-0.0001808-.9020914-0.0022315-.02533?出150.000395230.004581S-0.0028539-.03304? 岀17-0.013891-.15502? 桃出18-0.012822-.14959? 笊&巾iutccorrelationsnarkstwostandarderrorsStdError00.1162480.1307020.1378340.1427820.1468830.1502370.1540580.1558960.1560110.1581960.1604550.1617210.1625|40.1625840.1626400.1626410.1627320.164716圖7自相關(guān)圖顯示該序列自相關(guān)系數(shù)一直都比較小，1階開始控制在2倍的標準差范闈以內(nèi)，可以認為該序列自始自終都在零軸附近波動，這是隨即性非常強的平穩(wěn)時間序列。純隨機性檢驗見下圖：(圖8)AutocorrelationCheckforWhiteNoiseToLagChi-SquareDFPr>ChiSq AutQcorrelat ions 629.8?6<.00010.3630.2660.2270.2120.1890.2071238.58120.00010.1450.0360.1590.1630.1230.1021843.3?180.000?-0.002-0.0260.005-0.033-0.155-0.150圖8P值顯著小于0.05,可以認為這個擬合模型的殘差序列不屬于白躁聲序列選擇適當模型擬合該序列的發(fā)展。如呆序列平穩(wěn)且非白躁聲，選折適當模型擬合序列的發(fā)展模型識別如下圖(圖9)TheARIMAProcedureMinimumInformationCriterionLagsMA0昭1MA2昭3MA4昭5AR0-2.72095-2.76017-2.73002-2.67783-2.63698-2.61586AR1-2.82999-2.81521-2.78123-2.74199-2.69287-2.63872AR2-2.78313?2.7852-2.72898-2.68383-2.63748-2.5844AR3-2.75882-2.73983-2.68187-2.64734-2.61776-2.5937AR4-2.73063-2.69558-2.64141?2.61436-2.56306-2.54777AR5-2.69381-2.64278-2.59317-2.58439-2.54005-2.50554Errorseriesmodel:AR(8)MinimumTableValue：BIC(1?0)二-2.82999圖9最后一條信息顯示，在自相數(shù)遲階數(shù)小于等于5,移動平均延遲階數(shù)也小于等于5的所有ARNIA(p.q)模型中，EIC信息量相對最小的是ARN1A(1,0)模型，既AR(1)模型。利用擬合模型，預(yù)測該地區(qū)未來5年的谷物產(chǎn)量，預(yù)測結(jié)果如下圖(圖10)

ForecastsforvariablexObsForecastStdError95XConfidenceLimits750.63040.27930.08301.1779760.69170.29050.12241.2G10770.75580.29500.17771.3339780.82500.29720.24241.4076790.84470.29990.25691.4324圖10未來5年的谷物產(chǎn)量一次為0.63,0.69,0.75,0.83,0.8419現(xiàn)有201個連續(xù)的生產(chǎn)記錄，如表3-22所示81.989.47981.484.885.98880.382.683.580.285.287.283.584.382.984.782.981.583.487.781.879.685.877.989.785.486.380.783.890.584.582.486.78381.889.379.382.78879.687.883.679.583.388.486.684.679.78684.28384.883.681.885.988.283.587.283.787.38390.580.783.186.59077.584.784.687.280.586.182.685.484.782.881.983.686.88484.282.8838284.784.488.982.4838582.281.686.285.482.181.48585.884.283.586.58580.485.786.786.782.386.482.58279.586.780.591.781.683.985.684.878.489.98586.28385.484.484.586.285.683.285.783.580.182.288.6828585.285.384.382389.784.883.180.687.486.883.586.284.182.384.886.683.578.188.881.983.38087.283.386.679.584.182.290.886.579.78187.281.684.484.482.288.980.985.187.18476.582.785.183.390.48180.379.88983.780.987.381.185.686.68086.683.383.182386.780.2表3?22判斷該序列的平穩(wěn)性與純隨機性該序列的時序圖如下(圖11)

76I ■1 1 1 1 1 1 1 1 1 1I1 1 1 1 1 1 1 1 1I1 1 1 1 1 1 1 1 1I0 100 200 300tize圖11由時序圖顯示過去201個連續(xù)的生產(chǎn)記錄數(shù)據(jù)【韋I繞早84附近隨機波動，沒有明顯趨勢或周期，基本可以看成平穩(wěn)序列，為了穩(wěn)妥起見，做了如下自相關(guān)圖（圖12）Autocorrelationsasi^nceCorrelation?1987654321()1234567891StdError08.4064381.0000001-2.507186-.29825 10.0705352-1.012595-.12045?桃0.0765523-0.401869-.04780??0.07748940.9057320.107740.0776365-0.796389-.094730.07837661.3273770.157900.0789447-0.492395-.05857?岀0.08050080.1192190.014180.0807119-0.522226--06212?岀0.080724100.3881660.04623那：0.080861110.00685770.000820.08108312-0.523436-.06227:ft0.081083130.0128320.001530.081331140.7584200.090220.08133115-0.496505-.0590G:?0.081827160.5353480.06368*:0.08203917-0.467482-.055610.0822841S-0.487290-.05797?農(nóng)0.082471191.1099920.132040.08267420-0.715354-.085100.083716210.8274330.098440.08414622-0.039136--0046&0.08471723-1.018139-.121110.084718240.4481830.05331*:0.085575markstwostandarderrors圖12自相關(guān)圖顯示該序列自相關(guān)系數(shù)一直都比較小，1階開始控制在2倍的標準差范闈以內(nèi)，可以認為該序列自始自終都在零軸附近波動，這是隨即性非常強的平穩(wěn)時間序列。純隨機性檢驗見下圖：（圖13）AutocorrelationCheckforWhiteNoiseToLagChi-SquareDFPr>ChiSq"a11ug631.086<-0001-0.298-0.120-0.0480.108-0.0950.1581233.96120.0007-0.0590.014-O.OG20.0460.001-0.062183S.S3IS0.00300.0020.090-0.0590.064-0.056-0.05S2450-59240.00120.132-0.0850.098-0.005-0.1210.053圖13P值顯著小于0.05,可以認為這個擬合模型的殘差序列不屬于白躁聲序列如果序列平穩(wěn)且非白躁聲，選折適當模型擬合序列的發(fā)展模型識別如下圖(圖14)TheARIMAProcedureMinimumInformationCriterionLagsMA0MA1MA2MA3昭4MA5AR02.0773171.9606921.9626951