1、5% level-3.45276410% level-3.151911*MacKinnon (1996) one-sided p-values.单位根统计量ADF=-8.674646小于临界值,且P为0.0000,因此该序列不存在单位根,即该序列是平稳序列。由于趋势性会掩盖季节性,从lm图中可以看出,该序列有一定的季节性,为了分析季节性,对lm进行差分处理,进一步观察季节性:图3.3 dlm曲线图观察dlm 的自相关表:表3.3 dlm的自相关图Date: 11/02/14 Time: 22:35Sample: 2005M11 2014M09Included observations: 106
2、AutocorrelationPartial CorrelationACPACQ-StatProb*|. |1-0.56634.9340.000.|* |*|. |20.113-0.30536.341.|. |*|. |30.032-0.09336.4554-0.084-0.11437.24450.1050.01538.4946-0.18242.2967-0.15643.5638-0.058-0.17143.9549-0.019-0.19643.996100.110-0.04545.42911-0.242-0.32952.501.|* |120.3630.02368.51613-0.20273
3、.534140.1010.12574.815150.0040.14174.81716-0.161-0.08978.110.|* |170.2190.03784.25218-0.221-0.03690.623190.089-0.04691.66220-0.080-0.15892.516210.067-0.03993.115220.0680.05693.74923-0.231-0.130101.08240.3590.116119.0425-0.1890.123124.09260.034124.23270.059124.7428-0.1260.044127.08290.087-0.079128.21
4、30-0.0500.092128.5831-0.037128.7932-0.035-0.113128.97330.041-0.056129.24340.078-0.027130.21-0.215-0.197137.64360.3800.130161.26由dlm的自相关图可知,dlm在滞后期为12、24、36等差的自相关系数均显著异于零。因此该序列为以12为周期呈现季节性,而且季节自相关系数并没有衰减至零,因此为了考虑这种季节性,进行季节性差分,得新变量sdlm:观察sdlm的自相关图:表3.4 sdlm的自相关图40 94-0.50524.767. |. |*|. |-0.057-0.419
5、25.0820.073-0.29225.609. |* |0.16028.169.*|. |-0.264-0.12535.2520.098-0.11036.2440.01937.243-0.0410.08237.419-0.132-0.03839.2750.076-0.13939.902. |* |0.2270.24745.485-0.459-0.25968.6470.193-0.25172.7770.132-0.10174.753-0.14277.056-0.05377.3780.2330.09183.751-0.234-0.17990.2580.1020.05491.505-0.05291
6、.841-0.00993.714-0.0590.12094.150-0.0110.21594.166-0.032-0.17094.3010.088-0.13795.303-0.105-0.03496.7600.077-0.11697.562-0.054-0.17897.9670.01097.9820.03999.457-0.099104.060.071104.790.031-0.066104.93-0.144106.130.036106.32-0.102108.05Sdlm在滞后期24之后的季节ACF和PACF已衰减至零,下面对sdlm建立SARMA模型。3.2模型参数识别由表3.4 sdlm
7、的自相关图的自相关图可知,偏自相关系数在3阶后都落在两倍标准差的范围以内,即不显著异于零。自相关系数在1阶和12阶显著异于零。因此SARMA(p,q)模型中选择p、q均不超过3。此外,由于高阶移动平均模型估计较为困难而且自回归模型可以表示无穷阶的移动平均过程,因此Q尽可能取小。拟选择SARMA(1,0)(1,0)12、SARMA(1,0)(1,1)12、SARMA(1,1)(1,0)12、SARMA(1,1)(1,1)12、SARMA(2,0)(1,0)12、SARMA(2,0)(1,1)12、SARMA(3,0)(1,0)12、SARMA(3,0)(1,1)12八个模型来拟合sdlnm。3.
8、3模型参数估计以SARMA(1,0)(1,0)12模型为例,分析该模型的估计及残差的检验,其他模型类似。回归结果为:表3.5 SARMA(1,0)(1,0)12模型估计结果Dependent Variable: SDLMMethod: Least Squares50Sample (adjusted): 2008M01 2014M09 81 after adjustmentsConvergence achieved after 6 iterationsVariableCoefficientStd. ErrorProb.C-0.0053050.023352-0.2271650.8209AR(1)-
9、0.4908550.098580-4.979256SAR(12)-0.5485090.096987-5.655471R-squared0.448053Mean dependent var-0.004983Adjusted R-squared0.433901S.D. dependent var0.644876S.E. of regression0.485202Akaike info criterion1.427829Sum squared resid18.36280Schwarz criterion1.516512Log likelihood-54.82707Hannan-Quinn crite
10、r.1.463410F-statistic31.65901Durbin-Watson stat2.348799Prob(F-statistic)0.000000Inverted AR Roots.92+.25i.92-.25i.67+.67i.67-.67i.25-.92i.25+.92i-.25-.92i-.25+.92i-.49-.67-.67i-.92+.25i-.92-.25i由表3.3可知, AR(1)与sar(12)的P值均小于0.05,参数显著,可以通过检验。该模型AIC为1.427829,SC值为1.516512。回归结果的最后一部分表示该模型滞后多项式的反特征根,小于1,因此
11、该模型是平稳的。下面对残差进行检验。观察残差的自相关图:表3.6 SARMA(1,0)(1,0)12模型的残差检验结果由表3.6可知, 由Q统计量可知残差存在自相关性,P值远小于0.05,因此残差不满足白噪声的假设。将八个模型的估计结果进行汇总如下:表3.7 不同SARMA模型的特征汇总表AICSC平稳性可逆性残差是否满足白噪声SARMA(1,0)(1,0)12是否SARMA(1,0)(1,1)121.095434SARMA(1,1)(1,0)121.206181SARMA(1,1)(1,1)120.8624961.010301SARMA(2,0)(1,0)121.424354SARMA(2,
12、0)(1,1)121.0002481.149124SARMA(3,0)(1,0)121.2417641.391729SARMA(3,0)(1,1)120.959325综合来看,根据信息准则,应选择SARMA(1,1)(1,1)12对数据进行拟合是最优的。拟合结果为:表3.8 SARMA(1,1)(1,1)12模型估计结果 23:Convergence achieved after 13 iterationsMA Backcast: 2006M12 2007M12-0.0068210.002943-2.3177820.02320.0186630.1411680.1322030.8952-0.2016230.120638-1.6713130.0988MA(1)-0.8339470.080352-10.37865SMA(12)-0.8603910.041002-20.984270.7015100.6858000.3614759.930500-29.931070.92179744.653812.003373P
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