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1、第二章习题第一题代码如下data example2;input freq;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。从图中我们发现序列的自相关系数递
2、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=4 =0.41504K=5 =0.28008K=6 =0.152635SPSSAutocorrelationsSeries:freLagAutocorrelationStd. ErroraBox-Ljung StatisticValuedfSig.b1.850.20816.7321.0002.7
3、02.20228.7612.0003.556.19736.7623.0004.415.19141.5004.0005.280.18543.8005.0006.153.17844.5336.0007.034.17244.5727.0008-.074.16544.7718.0009-.170.15845.9219.00010-.252.15148.71310.00011-.319.14353.69311.00012-.370.13561.22012.00013-.403.12671.40913.00014-.416.11784.08714.00015-.408.10798.72915.000a.
4、The underlying process assumed is independence (white noise).b. Based on the asymptotic chi-square approximation.第二题代码如下data example2;input ppm;time=intnx(month,01jan1975d,_n_-1);format time monyy.;cards;330.45330.97331.64332.87333.61333.55331.90330.05328.58328.31329.41330.63331.63332.46333.36334.45
5、334.82334.32333.05330.87329.24328.87330.18331.50332.81333.23334.55335.82336.44335.99334.65332.41331.32330.73332.05333.53334.66335.07336.33337.39337.65337.57336.25334.39332.44332.25333.59334.76335.89336.44337.63338.54339.06338.95337.41335.71333.68333.69335.05336.53337.81338.16339.88340.57341.19340.87
6、339.25337.19335.49336.63337.74338.36;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;input ppm;time=intnx(month,1jan1975d,_n_-1);format t
7、ime monyy.;cards;330.45330.97331.64332.87333.61333.55331.90330.05328.58328.31329.41330.63331.63332.46333.36334.45334.82334.32333.05330.87329.24328.87330.18331.50332.81333.23334.55335.82336.44335.99334.65332.41331.32330.73332.05333.53334.66335.07336.33337.39337.65337.57336.25334.39332.44332.25333.593
8、34.76335.89336.44337.63338.54339.06338.95337.41335.71333.68333.69335.05336.53337.81338.16339.88340.57341.19340.87339.25337.19335.49336.63337.74338.36;proc arima data=example2_2;identify var=ppm nlag=24;run;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
9、的周期性质非常吻合。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 =0.90751K=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 StatisticValuedfSig.b1.908.11561.8031.0002.722.115101.4482.0003.513.114121.7313.0004.350.113131.320
10、4.0005.247.112136.1675.0006.203.111139.4976.0007.210.110143.1197.0008.264.110148.9348.0009.364.109160.1609.00010.485.108180.35010.00011.585.107210.19711.00012.602.106242.37612.00013.518.105266.64613.00014.369.104279.12414.00015.207.103283.11815.000a. The underlying process assumed is independence (w
11、hite noise).b. Based on the asymptotic chi-square approximation.第三题代码如下data example2;input mm;time=intnx(month,01jan1945d,_n_-1);format time monyy7.;cards;69.380.040.974.984.6101.1225.095.3100.648.3144.528.338.452.368.637.1148.6218.7131.6112.881.831.047.570.196.861.555.6171.7220.5119.463.2181.673.96
12、4.8166.948.0137.780.5105.289.9174.8124.086.4136.931.535.3112.343.0160.897.080.562.5158.27.6165.9106.792.263.226.277.052.3105.4144.349.5116.154.1148.6159.385.367.3112.859.4;proc gplot data =example2;plot mm*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的
13、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;input mm;time=intnx(month,1jan1945d,_n_-1);format time monyy7.;cards;69.380.040.974.984.6101.1225.095.3100.648.3144.528.338.452.368.637.1148.6218.7131.6112.881.831.047.570.196.861.555.6171.7220.5119.463.2181.673.964.8166.948.0137.780.5105.289.9174.8124.086.4136.931.535.3112.343.0160.897.080.562.5158.27.6165.9106.792.263.226.277.052.3105.4144.349.5116.154.1148.6
