对磨轮剖面资料的建模分析

对磨轮剖面资料的建模分析江南大学信计1103班陈鹭1301110301摘要：本文借助Eviews6.0软件使用B-J方法与P-W方法建立关于磨轮剖面资料的数学模型。使用B-J方法建模得到的结果为：X=0.944259X尸】。模型的适应性检验结果表明模型适合，且准确性较好。再通过P-W方法建模，ARMA（2,1）的模型是比较适合的，通过P值判断删去不显著的参数得到最终的模型为：X=1.210498X-0.406213X+a+0.694062a,。一、使用B-j方法建立数'亭模'型I1.1对原始数据平稳化的判断使用Eviews6.0软件做出原始数据的趋势图，如图（1）所示。由原始数据图可以看出，数据没有上升或下降趋势，也不表现出周期性，故初步判断该序列平稳。对原始数据进行ADF检验，如下图结果，表中T=-4.735499小于ADF表中1%〜5%水平下的临界值，故拒绝原假设，即不存在单位根，因此，该原始序列是平稳的。NullHypothesis:SER01hasaunitrootExogenous:Constant,Linea「T「enciLagLength:0[AutomaticbasedonAIC,MAXLAG=11)t-StatisticProb*AugmentedDickey-Fullerteststatistic-4.7354990.0014Testcriticalvalues:1%level-4.0007135%level-347255310%level-3.163450*MacKinnonf1996)one-sidedp-values.AugmentedDickey-FullerTestEquationDependentvariable:D(SER01)Method:LeastSquares□ate:12/01/13Time:15:57Sample(adjusted):20142036Includedobservations:73afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.SER01H)-0.4303320.10U32-4.7354990.0000C4.1135S21.1094793.7076710.0004@TREND(2013)0.0110720.0155370.7641130.4474R-squared0.242660Meandependentvar-0.094521AdjustedR-squared0.221022S.D.dependentvar3.134215S.E.ofreg「ession2.766250Akaikeinfocriterion4.913090Sumsquaredresid535.6497Schwarzcriterion5.00721SLoglikelihood-1763278Hannan-Quinncriter.4.950602F-statistic11.21439Durbin-Watsonstat1.717210ProbfF-statistic)0.0000602.模型识别使用Eviews6.0软件做出原始数据的自相关，偏自相关函数图像，如下图。取M=[v74]=8，当m=1时，、上1（A22折u+2p「。其在Pk«=2,3,4,5,6,7,8,9）中满足pJ<0.156的占|=62.5%当m=2时，在p（k=3,4,5,6,7,8,9,10）中满足p<[上（1+注p2）]2=0.150的占kknit=16=75.0%>68.3%，因而pk为2步截尾。可初步判定该序列X七适合MA（2）模型。对于偏自相关函数中序列，当k=1时，巾，。，...,©中满足kk223399cA>-^=0.232的个数占上=12.5%<31.7%,因而中在1步截尾。可初步判断该kk!N8kk

序列Xf也适合AR(1)模型，下面分别考虑两种模型的优劣。□ate:12/01/13Time:16:03Sample:20132036Includecfobservations:74AutocorrelationPartialCorrelationACFACQ-StatProb11110.5250.52521.1960.0001n11i20.233-0.05325.4510.00013i11i30.031-0.02525.9710.000|E11匚i4-0.097-0.16426.7300.000|匚111i5-0.166-0.05423.9790.000111160.0330.24729.0720.0001□11Ji70.1200.04230.2770.0001□I1]i30.1740.07132.3670.0001□111i90.140-0.06134.7680.00011ICi10-0.010-0.15934.7930.0001匚11i11-0.1200.00136.0790.0001匚11.1i12-0.155-0.03030.2490.0001匚11Ii13-0.1330.03339.0760.0001[11iU-0.0510.00340.1240.0001111i150.042-0.01540.2910.0001Ii11i160.049-0.02640.5270.001J111匚i17-0.0M-0.13240.7170.0011匚11[i18-0.159-0.09543.2490.001IC11Ii19-0.1730.040463140.000仁1(.1i20-0.190-0.04850.0600.0001匚111i21-0.159-0.03652.7500.000J111i22-0.0330.01552.3710.0001111i230.0490.00253.1370.0001]11i240.0500.01253.4150.0011]11]i250.0770.06S54.1020.0011]11]i260.0740.07354.7510.00113i1Ji270.0670.08655.2030.001|i11匚i23-0.033-0.16455.4170.002J111i29-0.0280.01355.5140.002J1111i30-0.027-0.04055.6090.003111]i310.0110.04955.6250.0041Ii1]i320.0570.07256.0530.0053.模型定阶对上面的序列进行残差方差图定阶，先做出模型从1阶开始的剩余平方和，并做出一定阶数范围内的残差方差图，如下。可以看出模型MA(2)阶数m从1上升至2时，残差方差减小较快；模型阶数m继续上升时，残差方差开始增大，可以判断合适的模型阶数为2。而在AR模型残差方差图中可以看出，适合的模型阶数为1。3200MA模型残差方差图AR模型残差方差图4.模型拟合与检验使用Eviews6.0软件得到如下结果进行分析:DependentVariable:SER01Method:LeastSquaresDate:12/01/13Time:17:16Sample:20132036Includedobservations:74Convergenceachievedafter13iterationsMASackcast:20112012VariableCoefficientStd.Errort-StatisticProb.M.A⑴1.2362150.09223813.395220.0000MA(2)0.641S650.0929046.9000930.0000R-squarecf-1.107575Meandependentvar9.633784AdjustedR-squared-1.136047S.D.dependentvar3.247434S.E.ofregression4.747035Akaikeinfocriterion5.979594Sumsquaredresid1622.507Schwarzcriterion6.041366Loglikelihood-219.2450Hannan-Quinncriter.6.004435Durbin-Watsonstat1.524675InvertedMARoots-.62-51i-.62+51i由上图可以知道MA(2)模型为：X=a-1.236215a1—0.641865a2IIIIIIII■303Q203020402050206020302090——SEtJOIF----72S.E对模型进行预测，如下图，可以看到预测值波动性大，不相等系数为IIIIIIII■303Q203020402050206020302090——SEtJOIF----72S.EF-DieDast:SEREFActifal:SERSF<jpEDastsample:2313205(2litcImdeElobEervatrane:50RootKaanSqirirecfError4.74SS2Bk拒anAbsoluteErrorB.SE4S4TWearAbs.PervertError45J23O5TheilIneiiKlityCneffkjent0.2753S1BiasProporttoF0.49&599VariaRDaProportion0.843了,CovarianoeProporttorO.M&53-D使用Eviews6.0软件得到如下结果进行分析:

DependentVariable:SER02Method:LeastSquaresDate:12；03/13Time:15:23Sample(adjusted}:20142086Includedobservations:73afteradjustmentsConvergenceachievedafter2iterationsVariableCoefficientStd.Errort-StatisticProb.AR⑴0.9442590.03537726.690930.0000R-squarecf0.093229Meandependentvar9.530822AdjustedR-squared0.093229S.D.dependentvar3.237563S.E.ofregression3.0S2960Akaikeinfocriterion5.10S261Sumsquaredresid684.3342Schwarzcriterion5.134637Loglikelihood-105.2690Hannan-Quinncriter.5.115765Durbin-Watsonstat2.119731Inverted.^RRoots.94有上图可以知道AR(1)模型为：X=0.944259X「a对模型进行预测，如下图，可以看到预测值波动性大，不相等系数为16%，其中协方差比列为97%，方差比列为0.3%。因此，认为AR(1)模型比MA(2)模型拟合更好，更适合。Forecast:SEROTFAct^l:SER01Forecastsample:231322®Acfjustedsample:20t4Forecast:SEROTFAct^l:SER01Forecastsample:231322®Acfjustedsample:20t42092Irtclucfedobser'i'aterts:7SRmtkteanSquaredError3.111817kteanAbsolutsError2.103155加职Ate.Percer?itError3240450TteilIrsq^lrtyCoeffiDEn-t9.355046BiasProportkjft0/D21S33VarianceProportiori0.W3422CovarianoeProportion0.97-4f*452CQ3203020502070208QI——SER01F-——72SE零均值化后所得数据如下：

3.9575-5.5425-5.5425-5.0425-6.5425-6.54250.45750.6575-0.54250.4575-1.04-2.540.957-2.04-2.540.957-0.04-2.542.4573.95725255252552525552.9575.4573.4571.457-0.540.9570.9571.9570.957-0.54555525555525-1.34-1.04-0.34-1.040.4574.9573.457-7.54-3.54-3.54252525255552525251.457-0.042.9574.2572.4572.4572.4573.4572.4574.457525555555554.9573.9572.757-2.54-2.54-2.54-3.042.9575.4572.957555252525255552.0571.4570.457-1.04-6.541.9571.9571.9571.457-0.545552525555525-7.04-2.54-3.54-2.944.4571.457-0.54-3.04-5.54-3.54252525255525252525模型拟合1使用Eviews6.0软件对模型ARMA（2n,2n-1）从n=1起进行拟合，改变阶数时剩余平方和变化列表如下：ARMA(6,5)ARMA(4,3)ARMA(2，1)576.3910655.0604496.3023由表可知：当n=2时的剩余平方和大于n=1时的剩余平方和，从n=1之后阶数增加而模型的剩余平方和不再显著减小，因此ARMA（2,1）是适合的。模型适应性检验拟合ARMA（2,1）模型，输出的模型适应性检验Q统计量为L(74)〜Q相伴概率（p值）87.02300.5341612.7560.690前8期的残差自相关的整体的心检验的相伴概率（p值）大于0.05，表明ARMA（2,1）模型是合适的。残差自相关如下图所示，滞后两期的残差自相关函数小于L96/yN=0.228，残差自相关检验也表明ARMA（2,1）模型是适合的。

Date:12/03713Time:16:09Sample:20132092Includedobservations:72AutocorrelationPartialCorrelationACFAC€l-StatProb11111110.0320.0320.07030.7301[11112-0.053-0.0540.29000.36511113-0.0010.0030.29000.9621□11匚14-0.123-0.1261.47570.0311匚1|匚15-0.200-0.1954.64540.4611I11]160.0810.0305.16900.5221111170.0440.0205.33020.6201□11□Ia0.1430.1437.02300.5341□112i90.1260.0838.36720.4981[1|E110-0.065-0.0818.72660.5581111111-0.0410.000S.B7510.6331匚1IE112-0.161-0.U911.16&0.5151C1r1113-0.100-0.02712.0640.5221111140.0200.01312.1010.59S11111150.0610.004124470.64511111160.0570.02312.75&0.6901]111170.073-0.01013.2690.71S1匚1iE110-0.123-0.12414.7720.6781[11119-0.059-0.01015.1280.7141111120-0.046-0.00915.3430.7561匚1iE121-0.149-0.10017.6570.6711111220.011-0.01017.6710.725111I11230.064-0.03518.1120.7511111240.013-0.01618.1300.79711111250.037-0.005182870.330111111260.04&0.03218.5100.0561]11□I270.0310.17719.2960.359|E1iE128-0.124-0.12321.1520.31911111129-0.0170.03721.1070.052111iE130-0.030-0.07421.3750.37611l11-0.004-0.026213780.90211111320.0060.026213030.923对于ARMA(2,1)模型，由P-W方法已无更低阶模型，故对序列作ARMA(2,1)建模分析如下：DepencfentVariable:SER01Method:LeastSquares□ate:12/17/13Time:22:15Samplefadjusted):20152036Includedobservations:72afteradjustmentsConvergenceachievedafter10iterationsMABackcast2014VariableCoefficientStd.Errort-StatisticProb.AR⑴1.2104930.2000476.0510590.0000AR⑵-0.40621S0.1362n-2.9021360.0040MA(1)-0.6940620.19S246-3.5010180.0003R-squared0366S2SMeandependentvar0.1158S3AdjustedR-squared0.348470S.D.dependentvar3.191351S.E.ofregression2.575976Akaikeinfocriterion4.771103Sumsquaredresid457.0601Schwa