乘积季节模型的sas例子

首先绘制该序列的时序图，如下所示：该时序图显示该序列有明显的长期趋势和以年为周期的季节效应。对该序列差分平稳，得到如下差分后的时序图：此时序图显示差分后序列类似平稳。接下来考察差分后序列的自相关图。如下：从自相关图可以看出，延迟12阶自相关系数显著大于2倍标准差，这说明差分后序列蕴含着非常显著的季节效应，但延迟24阶后就在2倍标准差范围以内了。而且延迟3阶的自相关系数也未在2倍标准差以内，说明差分后的序列仍存在短期相关性。接下来考察偏自相关图偏自相关图显示，延迟12阶的偏自相关系数同样显著大于2倍标准差，而且延迟24阶的偏自相关系数也未在2倍标准差以内。首先尝试拟合ARMA模型，但效果并不理想。于是综合考虑以上信息，决定拟合乘积模型ARIMA(1,1,1)(0,1,1)12使用最小二乘法得到该模型的口径为：模型检验的结果如下：从残差检验中可以看出，该模型顺利通过了残差检验。从参数检验的结果可以看出，各参数均显著。而且此模型用于预测时的标准差为44.35756。接下来对该数据进行X-11分析消除长期趋势影响得到的序列图如下：可以看出该序列季节效应很明显。消除季节效应得到的趋势图如下：使用移动平均的方法得到序列的趋势拟合图如下：从季节调整后序列中消除趋势项，得到随机波动项：从图中可以看出随机波动项很不规则，说明X-11过程对信息提取的很充分。附录：ARIMA程序：datatour;inputx@@;dif1_12=dif12(dif(x));time=intnx('month','1jan1998'd,_n_-1);formattimeyear4.;cards;508.02436.79491.89575.79514.97489.95539.13576.07512.51570.87542.48589.13545.94553.76559.39642.14581.58585.84626.38640.22590.32649.98646.98657.03645.06607.01664.5748.05674.42674.94743.54757.32712.28725.14696.36699.47717.15611.41753.26779.7707.87711.78745.38809.14741.32757.73749.71815.09740.7711.04839.54807.77787.92795.77849.37890.68865.12869.57841.91866.12848.43737.6785.14564.92543.6652.6776.94884.4807.58854.99828.42876.68808.73753.3855.16954.71877.47893.39959.03971.56917.45988.18935.21989.63938.06855.851027.771024.76995.14989.421076.111067.41988.771054.79990.781018.31998.85871.441002.981097.091002.391000.451090.41114.771043.771138.311042.091092.511022.98933.091089.81151.681072.551066.681149.141156.821123.131160.141109.11152.221080.95;procgplot;plotx*timedif1_12*time;symbolc=blacki=joinv=none;procarima;identifyvar=x(1,12);estimatep=1q=(1)(12)noint;forecastlead=0id=timeout=out;procgplotdata=out;plotx*time=1forecast*time=2/overlay;symbol1c=blacki=nonev=doth=0.2;symbol2c=redi=joinv=none;run;X-11过程程序：datatour;inputy@@;t=intnx('month','1jan1998'd,_n_-1);formattyear4.;cards;508.02436.79491.89575.79514.97489.95539.13576.07512.51570.87542.48589.13545.94553.76559.39642.14581.58585.84626.38640.22590.32649.98646.98657.03645.06607.01664.5748.05674.42674.94743.54757.32712.28725.14696.36699.47717.15611.41753.26779.7707.87711.78745.38809.14741.32757.73749.71815.09740.7711.04839.54807.77787.92795.77849.37890.68865.12869.57841.91866.12848.43737.6785.14564.92543.6652.6776.94884.4807.58854.99828.42876.68808.73753.3855.16954.71877.47893.39959.03971.56917.45988.18935.21989.63938.06855.851027.771024.76995.14989.421076.111067.41988.771054.79990.781018.31998.85871.441002.981097.091002.391000.451090.41114.771043.771138.311042.091092.511022.98933.091089.81151.681072.551066.681149.141156.821123.131160.141109.11152.221080.95;procx11data=tour;monthlydate=t;vary;outputout=outb1=yd10=seasond11=adjustedd12=trendd13=irr;procgplotdata=out;plotseason*t=2adjusted*t=2trend*t=2irr*t=2;ploty*t=1adjusted*t=2/overlay;symbol1c=bluei=joinv=star;