时间序列分析习题及答案

第一题：

1、绘制时序图：

data ex1_1; input x@@ ;

time=intnx('month','01jul2004'd,_n_-1); format time date. ; cards;

153 134 145 117 187 175 203 178 234 243 189 149 212 227 214 178 300 298 295 248 221 256 220 202 201 237 231 162 175 165 174 135 123 124 119 120 104 106 85 96 85 87 67 90 78 74 75 63 ;

proc gplot data=ex1_1; plot x*time=1;

symbol1 c=black v=star i=join; run;

时序图：

2、绘制自相关图：

data ex1_1; input x@@ ;

time=intnx('month','01jul2004'd,_n_-1); format time date. ; cards;

153 134 145 117 187 175 203 178 234 243 189 149 212 227 214 178 300 298 295 248 221 256 220 202 201 237 231 162 175 165 174 135 123 124 119 120 104 106 85 96 85 87 67 90 78 74 75 63

1

;

proc arima data=ex1_1; identify var=x; run;

样本自相关图：

白噪声检验输出结果：

因为P值小于α，所以该序列为非白噪声序列，根据时序图看出数据并不在一个常数值附近随机波动，后期有递减的趋势，所以不是平稳序列。

第二题：

1、选择拟合模型 方法一：

首先绘制该序列的时序图，直观检验序列平稳性。时序图显示序列没有显著的非平稳特征。在考察自相关图和偏自相关图，自相关图显示延迟1阶、6阶、19阶的自相关系数在2倍标准差范围之外，其他阶数的自相关系数都在2倍标准差范围内波动，根据自相关系数的这个特点可以判断该序列具有短期相关性，进一步确定序列平稳。同时可以认为该序列自相关系数1阶截尾。偏自相关系数可以看为拖尾，综合该序列自相关系数和偏自相关系数的性质，为拟合模型定阶为MA(1)模型。

绘制时序图

data ex1_2;

2

input x@@ ;

time=intnx('month','01jul2004'd,_n_-1); format time date. ; cards;

81.9 89.4 79.0 81.4 84.8 85.9 88.0 80.3 82.6 83.5 80.2 85.2 87.2 83.5 84.3 82.9 84.7 82.9 81.5 83.4 87.7 81.8 79.6 85.8 77.9 89.7 85.4 86.3 80.7 83.8 90.5 84.5 82.4 86.7 83.0 81.8 89.3 79.3 82.7 88.0 79.6 87.8 83.6 79.5 83.3 88.4 86.6 84.6 79.7 86.0 84.2 83.0 84.8 83.6 81.8 85.9 88.2 83.5 87.2 83.7 87.3 83.0 90.5 80.7 83.1 86.5 90.0 77.5 84.7 84.6 87.2 80.5 86.1 82.6 85.4 84.7 82.8 81.9 83.6 86.8 84.0 84.2 82.8 83.0 82.0 84.7 84.4 88.9 82.4 83.0 85.0 82.2 81.6 86.2 85.4 82.1 81.4 85.0 85.8 84.2 83.5 86.5 85.0 80.4 85.7 86.7 86.7 82.3 86.4 82.5 82.0 79.5 86.7 80.5 91.7 81.6 83.9 85.6 84.8 78.4 89.9 85.0 86.2 83.0 85.4 84.4 84.5 86.2 85.6 83.2 85.7 83.5 80.1 82.2 88.6 82.0 85.0 85.2 85.3 84.3 82.3 89.7 84.8 83.1 80.6 87.4 86.8 83.5 86.2 84.1 82.3 84.8 86.6 83.5 78.1 88.8 81.9 83.3 80.0 87.2 83.3 86.6 79.5 84.1 82.2 90.8 86.5 79.7 81.0 87.2 81.6 84.4 84.4 82.2 88.9 80.9 85.1 87.1 84.0 76.5 82.7 85.1 83.3 90.4 81.0 80.3 79.8 89.0 83.7 80.9 87.3 81.1 85.6 86.6 80.0 86.6 83.3 83.1 82.3 86.7 80.2 ;

proc gplot data=ex1_2; plot x*time=1;

symbol1 c=black v=star i=join; run;

时序图

绘制自相关图、偏自相关图

3

data ex1_2; input x@@ ;

time=intnx('month','01jul2004'd,_n_-1); format time date. ; cards;

81.9 89.4 79.0 81.4 84.8 85.9 88.0 80.3 82.6 83.5 80.2 85.2 87.2 83.5 84.3 82.9 84.7 82.9 81.5 83.4 87.7 81.8 79.6 85.8 77.9 89.7 85.4 86.3 80.7 83.8 90.5 84.5 82.4 86.7 83.0 81.8 89.3 79.3 82.7 88.0 79.6 87.8 83.6 79.5 83.3 88.4 86.6 84.6 79.7 86.0 84.2 83.0 84.8 83.6 81.8 85.9 88.2 83.5 87.2 83.7 87.3 83.0 90.5 80.7 83.1 86.5 90.0 77.5 84.7 84.6 87.2 80.5 86.1 82.6 85.4 84.7 82.8 81.9 83.6 86.8 84.0 84.2 82.8 83.0 82.0 84.7 84.4 88.9 82.4 83.0 85.0 82.2 81.6 86.2 85.4 82.1 81.4 85.0 85.8 84.2 83.5 86.5 85.0 80.4 85.7 86.7 86.7 82.3 86.4 82.5 82.0 79.5 86.7 80.5 91.7 81.6 83.9 85.6 84.8 78.4 89.9 85.0 86.2 83.0 85.4 84.4 84.5 86.2 85.6 83.2 85.7 83.5 80.1 82.2 88.6 82.0 85.0 85.2 85.3 84.3 82.3 89.7 84.8 83.1 80.6 87.4 86.8 83.5 86.2 84.1 82.3 84.8 86.6 83.5 78.1 88.8 81.9 83.3 80.0 87.2 83.3 86.6 79.5 84.1 82.2 90.8 86.5 79.7 81.0 87.2 81.6 84.4 84.4 82.2 88.9 80.9 85.1 87.1 84.0 76.5 82.7 85.1 83.3 90.4 81.0 80.3 79.8 89.0 83.7 80.9 87.3 81.1 85.6 86.6 80.0 86.6 83.3 83.1 82.3 86.7 80.2 ;

proc arima data=ex1_2; identify var=x; run;

自相关图

偏自相关图

4

方法二：相对最优定阶

data ex1_2; input x@@ ;

time=intnx('month','01jul2004'd,_n_-1); format time date. ; cards;

81.9 89.4 79.0 81.4 84.8 85.9 88.0 80.3 82.6 83.5 80.2 85.2 87.2 83.5 84.3 82.9 84.7 82.9 81.5 83.4 87.7 81.8 79.6 85.8 77.9 89.7 85.4 86.3 80.7 83.8 90.5 84.5 82.4 86.7 83.0 81.8 89.3 79.3 82.7 88.0 79.6 87.8 83.6 79.5 83.3 88.4 86.6 84.6 79.7 86.0 84.2 83.0 84.8 83.6 81.8 85.9 88.2 83.5 87.2 83.7 87.3 83.0 90.5 80.7 83.1 86.5 90.0 77.5 84.7 84.6 87.2 80.5 86.1 82.6 85.4 84.7 82.8 81.9 83.6 86.8 84.0 84.2 82.8 83.0 82.0 84.7 84.4 88.9 82.4 83.0 85.0 82.2 81.6 86.2 85.4 82.1 81.4 85.0 85.8 84.2 83.5 86.5 85.0 80.4 85.7 86.7 86.7 82.3 86.4 82.5 82.0 79.5 86.7 80.5 91.7 81.6 83.9 85.6 84.8 78.4 89.9 85.0 86.2 83.0 85.4 84.4 84.5 86.2 85.6 83.2 85.7 83.5 80.1 82.2 88.6 82.0 85.0 85.2 85.3 84.3 82.3 89.7 84.8 83.1 80.6 87.4 86.8 83.5 86.2 84.1 82.3 84.8 86.6 83.5 78.1 88.8 81.9 83.3 80.0 87.2 83.3 86.6 79.5 84.1 82.2 90.8 86.5 79.7 81.0 87.2 81.6 84.4 84.4 82.2 88.9 80.9 85.1 87.1 84.0 76.5 82.7 85.1 83.3 90.4 81.0 80.3 79.8 89.0 83.7 80.9 87.3 81.1 85.6 86.6 80.0 86.6 83.3 83.1 82.3 86.7 80.2 ;

proc arima data=ex1_2;

identify var=x nlag=8 minic p=(0:5) q=(0:5); run;

5

最后一条信息显示，在自相关延迟阶数小于等于5，移动平均延迟阶数也小于等于5的所有ARMA(p，q)模型中，BIC信息量相对最小的是ARMA（0,1）模型，即MA(1)模型。

2、估计模型中未知参数的值，

data ex1_2; input x@@ ;

time=intnx('month','01jul2004'd,_n_-1); format time date. ; cards;

81.9 89.4 79.0 81.4 84.8 85.9 88.0 80.3 82.6 83.5 80.2 85.2 87.2 83.5 84.3 82.9 84.7 82.9 81.5 83.4 87.7 81.8 79.6 85.8 77.9 89.7 85.4 86.3 80.7 83.8 90.5 84.5 82.4 86.7 83.0 81.8 89.3 79.3 82.7 88.0 79.6 87.8 83.6 79.5 83.3 88.4 86.6 84.6 79.7 86.0 84.2 83.0 84.8 83.6 81.8 85.9 88.2 83.5 87.2 83.7 87.3 83.0 90.5 80.7 83.1 86.5 90.0 77.5 84.7 84.6 87.2 80.5 86.1 82.6 85.4 84.7 82.8 81.9 83.6 86.8 84.0 84.2 82.8 83.0 82.0 84.7 84.4 88.9 82.4 83.0 85.0 82.2 81.6 86.2 85.4 82.1 81.4 85.0 85.8 84.2 83.5 86.5 85.0 80.4 85.7 86.7 86.7 82.3 86.4 82.5 82.0 79.5 86.7 80.5 91.7 81.6 83.9 85.6 84.8 78.4 89.9 85.0 86.2 83.0 85.4 84.4 84.5 86.2 85.6 83.2 85.7 83.5 80.1 82.2 88.6 82.0 85.0 85.2 85.3 84.3 82.3 89.7 84.8 83.1 80.6 87.4 86.8 83.5 86.2 84.1 82.3 84.8 86.6 83.5 78.1 88.8 81.9 83.3 80.0 87.2 83.3 86.6 79.5 84.1 82.2 90.8 86.5 79.7 81.0 87.2 81.6 84.4 84.4 82.2 88.9 80.9 85.1 87.1 84.0 76.5 82.7 85.1 83.3 90.4 81.0 80.3 79.8 89.0 83.7 80.9 87.3 81.1 85.6 86.6 80.0 86.6 83.3 83.1 82.3 86.7 80.2 ;

proc arima data=ex1_2; identify var=x; estimate q=1; run;

输出的未知参数估计结果如图：

3、模型检验

通过计算得到t统计量的p值均显著大于α，所以该拟合模型显著成立。 4、序列预测

6

data ex1_2; input x@@ ;

time=intnx('month','01jul2004'd,_n_-1); format time date. ; cards;

81.9 89.4 79.0 81.4 84.8 85.9 88.0 80.3 82.6 83.5 80.2 85.2 87.2 83.5 84.3 82.9 84.7 82.9 81.5 83.4 87.7 81.8 79.6 85.8 77.9 89.7 85.4 86.3 80.7 83.8 90.5 84.5 82.4 86.7 83.0 81.8 89.3 79.3 82.7 88.0 79.6 87.8 83.6 79.5 83.3 88.4 86.6 84.6 79.7 86.0 84.2 83.0 84.8 83.6 81.8 85.9 88.2 83.5 87.2 83.7 87.3 83.0 90.5 80.7 83.1 86.5 90.0 77.5 84.7 84.6 87.2 80.5 86.1 82.6 85.4 84.7 82.8 81.9 83.6 86.8 84.0 84.2 82.8 83.0 82.0 84.7 84.4 88.9 82.4 83.0 85.0 82.2 81.6 86.2 85.4 82.1 81.4 85.0 85.8 84.2 83.5 86.5 85.0 80.4 85.7 86.7 86.7 82.3 86.4 82.5 82.0 79.5 86.7 80.5 91.7 81.6 83.9 85.6 84.8 78.4 89.9 85.0 86.2 83.0 85.4 84.4 84.5 86.2 85.6 83.2 85.7 83.5 80.1 82.2 88.6 82.0 85.0 85.2 85.3 84.3 82.3 89.7 84.8 83.1 80.6 87.4 86.8 83.5 86.2 84.1 82.3 84.8 86.6 83.5 78.1 88.8 81.9 83.3 80.0 87.2 83.3 86.6 79.5 84.1 82.2 90.8 86.5 79.7 81.0 87.2 81.6 84.4 84.4 82.2 88.9 80.9 85.1 87.1 84.0 76.5 82.7 85.1 83.3 90.4 81.0 80.3 79.8 89.0 83.7 80.9 87.3 81.1 85.6 86.6 80.0 86.6 83.3 83.1 82.3 86.7 80.2 ;

proc arima data=ex1_2; identify var=x; estimate q=1;

forecast lead=5 id=time out=results; run;

该输出结果中从左到右分别为序列值的序号、预测值、预测值的标准差、95%

7

的置信下限、95%的置信上限。

第三题：

1、选择拟合模型 方法一：

首先绘制该序列的时序图，直观检验序列平稳性。根据时序图看出数据并不在一个常数值附近随机波动，有递增的趋势，所以不是平稳序列。在考察自相关图和偏自相关图，可以认为该序列自相关系数拖尾，偏自相关系数1阶截尾，综合该序列自相关系数和偏自相关系数的性质，为拟合模型定阶为AR(1)模型。

绘制时序图

data ex1_3; input x@@ ;

time=intnx('month','01jan2001'd,_n_-1); format time date. ; cards;

3333 3047.1 2876.1 2820.9 2929.6 2908.7 2851.4 3065.7 3136.9 3347.3 3421.7 4033.3

3552 3416 3197.4 3163.3 3320.5 3302.8 3244.2 3284.4 3627.2 3815.2 3831.1 4270.2

3907 3706.4 3494.8 3406.9 3463.3 3576.9 3562.1 3609.6 3971.8 4204.4 4202.7 4735.7

4753 4328.3 4213.4 4156.2 4343.3 4371.1 4378.8 4480.7 4876 5183.2 5257.1 6089.2

5301 5012.2 4799.1 4663.3 4899.2 4935 4934.9 5040.8 5495.2 5846.6 5909 6850.4

6642 6001.9 5796.7 5774.6 6175.6 6057.8 6012.2 6077.4 6553.6 6997.7 6821.7 7499.2

7488 7013.7 6685.8 6672.5 7157.5 7026 6998.2 7116.6 7668.4 8263 8104.7 9015.3

9077 8354.7 8123.2 8142 8703.5 8642 8628.8 8767.7 9446.5 10082.7 9790.8 10728.5

10757 9323.8 9317.6 9343.2 10028.4 9941.6 9936.5 10115.6 10912.8 11717.6 11339 12610

12718 12334.2 11321.7 11510.4 12455.1 12329.9 12252.8 12569.8 13536.5 14284.8 13910.9 15329.5

15249 13769.1 13588 13649 14696.8 14565.1 14408 14705 15865.1 16546.4 16128.9 17739.7 ;

proc gplot data=ex1_3; plot x*time=1;

8

symbol1 c=black v=star i=join; run;

时序图

绘制自相关图、偏自相关图

data ex1_3; input x@@ ;

time=intnx('month','01jan2001'd,_n_-1); format time date. ; cards;

3333 3047.1 2876.1 2820.9 2929.6 2908.7 2851.4 3065.7 3136.9 3347.3 3421.7 4033.3

3552 3416 3197.4 3163.3 3320.5 3302.8 3244.2 3284.4 3627.2 3815.2 3831.1 4270.2

3907 3706.4 3494.8 3406.9 3463.3 3576.9 3562.1 3609.6 3971.8 4204.4 4202.7 4735.7

4753 4328.3 4213.4 4156.2 4343.3 4371.1 4378.8 4480.7 4876 5183.2 5257.1 6089.2

5301 5012.2 4799.1 4663.3 4899.2 4935 4934.9 5040.8 5495.2 5846.6 5909 6850.4

6642 6001.9 5796.7 5774.6 6175.6 6057.8 6012.2 6077.4 6553.6 6997.7 6821.7 7499.2

7488 7013.7 6685.8 6672.5 7157.5 7026 6998.2 7116.6 7668.4 8263 8104.7 9015.3

9077 8354.7 8123.2 8142 8703.5 8642 8628.8 8767.7 9446.5 10082.7 9790.8 10728.5

10757 9323.8 9317.6 9343.2 10028.4 9941.6 9936.5 10115.6 10912.8 11717.6 11339 12610

12718 12334.2 11321.7 11510.4 12455.1 12329.9 12252.8 12569.8 13536.5 14284.8 13910.9 15329.5

9

15249 13769.1 13588 13649 14696.8 14565.1 14408 14705 15865.1 16546.4 16128.9 17739.7 ;

proc arima data=ex1_3; identify var=x; run;

自相关图

偏自相关图

10

方法二：相对最优定阶

data ex1_3; input x@@ ;

time=intnx('month','01Jan2001'd,_n_-1); format time date. ; cards;

3333 3047.1 2876.1 2820.9 2929.6 2908.7 2851.4 3065.7 3136.9 3347.3 3421.7 4033.3

3552 3416 3197.4 3163.3 3320.5 3302.8 3244.2 3284.4 3627.2 3815.2 3831.1 4270.2

3907 3706.4 3494.8 3406.9 3463.3 3576.9 3562.1 3609.6 3971.8 4204.4 4202.7 4735.7

4753 4328.3 4213.4 4156.2 4343.3 4371.1 4378.8 4480.7 4876 5183.2 5257.1 6089.2

5301 5012.2 4799.1 4663.3 4899.2 4935 4934.9 5040.8 5495.2 5846.6 5909 6850.4

6642 6001.9 5796.7 5774.6 6175.6 6057.8 6012.2 6077.4 6553.6 6997.7 6821.7 7499.2

7488 7013.7 6685.8 6672.5 7157.5 7026 6998.2 7116.6 7668.4 8263 8104.7 9015.3

9077 8354.7 8123.2 8142 8703.5 8642 8628.8 8767.7 9446.5 10082.7 9790.8 10728.5

10757 9323.8 9317.6 9343.2 10028.4 9941.6 9936.5 10115.6 10912.8 11717.6 11339 12610

12718 12334.2 11321.7 11510.4 12455.1 12329.9 12252.8 12569.8 13536.5 14284.8 13910.9 15329.5

15249 13769.1 13588 13649 14696.8 14565.1 14408 14705 15865.1 16546.4 16128.9 17739.7 ;

proc arima data=ex1_3;

identify var=x nlag=8 minic p=(0:5) q=(0:5); run;

最后一条信息显示，在自相关延迟阶数小于等于5，移动平均延迟阶数也小

11

于等于5的所有ARMA(p，q)模型中，从BIC信息量相对最小的是ARMA（1,0）模型，即AR(1)模型。

3、估计模型中未知参数的值，

data ex1_3; input x@@ ;

time=intnx('month','01Jan2001'd,_n_-1); format time date. ; cards;

3333 3047.1 2876.1 2820.9 2929.6 2908.7 2851.4 3065.7 3136.9 3347.3 3421.7 4033.3

3552 3416 3197.4 3163.3 3320.5 3302.8 3244.2 3284.4 3627.2 3815.2 3831.1 4270.2

3907 3706.4 3494.8 3406.9 3463.3 3576.9 3562.1 3609.6 3971.8 4204.4 4202.7 4735.7

4753 4328.3 4213.4 4156.2 4343.3 4371.1 4378.8 4480.7 4876 5183.2 5257.1 6089.2

5301 5012.2 4799.1 4663.3 4899.2 4935 4934.9 5040.8 5495.2 5846.6 5909 6850.4

6642 6001.9 5796.7 5774.6 6175.6 6057.8 6012.2 6077.4 6553.6 6997.7 6821.7 7499.2

7488 7013.7 6685.8 6672.5 7157.5 7026 6998.2 7116.6 7668.4 8263 8104.7 9015.3

9077 8354.7 8123.2 8142 8703.5 8642 8628.8 8767.7 9446.5 10082.7 9790.8 10728.5

10757 9323.8 9317.6 9343.2 10028.4 9941.6 9936.5 10115.6 10912.8 11717.6 11339 12610

12718 12334.2 11321.7 11510.4 12455.1 12329.9 12252.8 12569.8 13536.5 14284.8 13910.9 15329.5

15249 13769.1 13588 13649 14696.8 14565.1 14408 14705 15865.1 16546.4 16128.9 17739.7 ;

proc arima data=ex1_3; identify var=x; estimate p=1; run;

输出的未知参数估计结果如图：

12

4、模型检验

通过计算得到t统计量的p值均显著大于α，所以该拟合模型显著成立。 5、序列预测

data ex1_3; input x@@ ;

time=intnx('month','01jan2001'd,_n_-1); format time date. ; cards;

3333 3047.1 2876.1 2820.9 2929.6 2908.7 2851.4 3065.7 3136.9 3347.3 3421.7 4033.3

3552 3416 3197.4 3163.3 3320.5 3302.8 3244.2 3284.4 3627.2 3815.2 3831.1 4270.2

3907 3706.4 3494.8 3406.9 3463.3 3576.9 3562.1 3609.6 3971.8 4204.4 4202.7 4735.7

4753 4328.3 4213.4 4156.2 4343.3 4371.1 4378.8 4480.7 4876 5183.2 5257.1 6089.2

5301 5012.2 4799.1 4663.3 4899.2 4935 4934.9 5040.8 5495.2 5846.6 5909 6850.4

6642 6001.9 5796.7 5774.6 6175.6 6057.8 6012.2 6077.4 6553.6 6997.7 6821.7 7499.2

7488 7013.7 6685.8 6672.5 7157.5 7026 6998.2 7116.6 7668.4 8263 8104.7 9015.3

9077 8354.7 8123.2 8142 8703.5 8642 8628.8 8767.7 9446.5 10082.7 9790.8 10728.5

10757 9323.8 9317.6 9343.2 10028.4 9941.6 9936.5 10115.6 10912.8 11717.6 11339 12610

12718 12334.2 11321.7 11510.4 12455.1 12329.9 12252.8 12569.8 13536.5 14284.8 13910.9 15329.5

15249 13769.1 13588 13649 14696.8 14565.1 14408 14705 15865.1 16546.4 16128.9 17739.7 ;

proc arima data=ex1_3; identify var=x; estimate p=1;

forecast lead=3 id=time out=results; run；

该输出结果中从左到右分别为序列值的序号、预测值、预测值的标准差、95%的

13

置信下限、95%的置信上限。

6、绘制拟合效果图

data ex1_3; input x@@ ;

time=intnx('month','01jan2001'd,_n_-1); format time date. ; cards;

3333 3047.1 2876.1 2820.9 2929.6 2908.7 2851.4 3065.7 3136.9 3347.3 3421.7 4033.3

3552 3416 3197.4 3163.3 3320.5 3302.8 3244.2 3284.4 3627.2 3815.2 3831.1 4270.2

3907 3706.4 3494.8 3406.9 3463.3 3576.9 3562.1 3609.6 3971.8 4204.4 4202.7 4735.7

4753 4328.3 4213.4 4156.2 4343.3 4371.1 4378.8 4480.7 4876 5183.2 5257.1 6089.2

5301 5012.2 4799.1 4663.3 4899.2 4935 4934.9 5040.8 5495.2 5846.6 5909 6850.4

6642 6001.9 5796.7 5774.6 6175.6 6057.8 6012.2 6077.4 6553.6 6997.7 6821.7 7499.2

7488 7013.7 6685.8 6672.5 7157.5 7026 6998.2 7116.6 7668.4 8263 8104.7 9015.3

9077 8354.7 8123.2 8142 8703.5 8642 8628.8 8767.7 9446.5 10082.7 9790.8 10728.5

10757 9323.8 9317.6 9343.2 10028.4 9941.6 9936.5 10115.6 10912.8 11717.6 11339 12610

12718 12334.2 11321.7 11510.4 12455.1 12329.9 12252.8 12569.8 13536.5 14284.8 13910.9 15329.5

15249 13769.1 13588 13649 14696.8 14565.1 14408 14705 15865.1 16546.4 16128.9 17739.7 ;

proc gplot data=results;

plot x*time=1 forecast*time=2 l95*time=3 u95*time=3/overlay; symbol1 c=black i=none v=star; symbol2 c=red i=join v=none;

symbol3 c=green i=join v=none l=32 ; run； 第三题

data e5_12; input shxf@@;

dshxf=dif(dif(shxf)); t=_n_;

14

cards; 3333 3047.1 2876.1 2820.9 2929.6 2908.7 2851.4 3065.7 3136.9 3347.3 3421.7 4033.3 3552 3416 3197.4 3163.3 3320.5 3302.8 3244.2 3284.4 3627.2 3815.2 3831.1 4270.2 3907 3706.4 3494.8 3406.9 3463.3 3576.9 3562.1 3609.6 3971.8 4204.4 4202.7 4735.7

4753 4328.3 4213.4 4156.2 4343.3 4371.1 4378.8 4480.7 4876 5183.2 5257.1 6089.2

5301 5012.2 4799.1 4663.3 4899.2 4935 4934.9 5040.8 5495.2 5846.6 5909 6850.4 6642 6001.9 5796.7 5774.6 6175.6 6057.8 6012.2 6077.4 6553.6 6997.7 6821.7 7499.2

7488 7013.7 6685.8 6672.5 7157.5 7026 6998.2 7116.6 7668.4 8263 8104.7 9015.3

9077 8354.7 8123.2 8142 8703.5 8642 8628.8 8767.7 9446.5 10082.7 9790.8 10728.5

10757 9323.8 9317.6 9343.2 10028.4 9941.6 9936.5 10115.6 10912.8 11717.6 11339 12610

12718 12334.2 11321.7 11510.4 12455.1 12329.9 12252.8 12569.8 13536.5 14284.8 13910.9 15329.5

15249 13769.1 13588 13649 14696.8 14565.1 14408 14705 15865.1 16546.4 16128.9 17739.7 ;

proc gplot; plot dshxf*t;

symbol v=star c=black i=join; proc arima;

identify var=shxf(2) minic p=(0:5) q=(0:5); estimate p=5 q=5; forecast lead=4; run; 改过

data e5_12; input x@@; dif2=dif(dif(x)); t=_n_; cards;

3333 3047.1 2876.1 2820.9 2929.6 2908.7 2851.4 3065.7 3136.9 3347.3 3421.7 4033.3 3552 3416 3197.4 3163.3 3320.5 3302.8 3244.2 3284.4 3627.2 3815.2 3831.1 4270.2

3907 3706.4 3494.8 3406.9 3463.3 3576.9 3562.1 3609.6 3971.8 4204.4 4202.7 4735.7 4753 4328.3 4213.4 4156.2 4343.3 4371.1 4378.8 4480.7 4876 5183.2 5257.1 6089.2 5301 5012.2 4799.1 4663.3 4899.2 4935 4934.9 5040.8 5495.2 5846.6 5909 6850.4

15

6642 6001.9 5796.7 5774.6 6175.6 6057.8 6012.2 6077.4 6553.6 6997.7 6821.7 7499.2 7488 7013.7 6685.8 6672.5 7157.5 7026 6998.2 7116.6 7668.4 8263 8104.7 9015.3 9077 8354.7 8123.2 8142 8703.5 8642 8628.8 8767.7 9446.5 10082.7 9790.8 10728.5 10757 9323.8 9317.6 9343.2 10028.4 9941.6 9936.5 10115.6 10912.8 11717.6 11339 12610

12718 12334.2 11321.7 11510.4 12455.1 12329.9 12252.8 12569.8 13536.5 14284.8 13910.9 15329.5 15249 13769.1 13588 13649 14696.8 14565.1 14408 14705 15865.1 16546.4 16128.9 17739.7 ;

proc gplot; plot dif1*t;

symbol v=star c=blue i=join; proc arima;

identify var=shxf(2) minic p=(0:5) q=(0:5); estimate p=5 q=5; forecast lead=4; run;

画1阶差分后时序图

data e5_12; input x@@; dif1=dif(x); t=_n_; cards;

3333 3047.1 2876.1 2820.9 2929.6 2908.7 2851.4 3065.7 3136.9 3347.3 3421.7 4033.3 3552 3416 3197.4 3163.3 3320.5 3302.8 3244.2 3284.4 3627.2 3815.2 3831.1 4270.2

3907 3706.4 3494.8 3406.9 3463.3 3576.9 3562.1 3609.6 3971.8 4204.4 4202.7 4735.7 4753 4328.3 4213.4 4156.2 4343.3 4371.1 4378.8 4480.7 4876 5183.2 5257.1 6089.2 5301 5012.2 4799.1 4663.3 4899.2 4935 4934.9 5040.8 5495.2 5846.6 5909 6850.4 6642 6001.9 5796.7 5774.6 6175.6 6057.8 6012.2 6077.4 6553.6 6997.7 6821.7 7499.2 7488 7013.7 6685.8 6672.5 7157.5 7026 6998.2 7116.6 7668.4 8263 8104.7 9015.3 9077 8354.7 8123.2 8142 8703.5 8642 8628.8 8767.7 9446.5 10082.7 9790.8 10728.5 10757 9323.8 9317.6 9343.2 10028.4 9941.6 9936.5 10115.6 10912.8 11717.6 11339 12610

12718 12334.2 11321.7 11510.4 12455.1 12329.9 12252.8 12569.8 13536.5 14284.8 13910.9 15329.5 15249 13769.1 13588 13649 14696.8 14565.1 14408 14705 15865.1 16546.4 16128.9 17739.7 ;

proc gplot; plot dif1*t;

symbol v=star c=blue i=join; run;

画12步差分后时序图

data e5_12; input x@@; dif1=dif(x); t=_n_;

16

cards;

3333 3047.1 2876.1 2820.9 2929.6 2908.7 2851.4 3065.7 3136.9 3347.3 3421.7 4033.3 3552 3416 3197.4 3163.3 3320.5 3302.8 3244.2 3284.4 3627.2 3815.2 3831.1 4270.2

3907 3706.4 3494.8 3406.9 3463.3 3576.9 3562.1 3609.6 3971.8 4204.4 4202.7 4735.7 4753 4328.3 4213.4 4156.2 4343.3 4371.1 4378.8 4480.7 4876 5183.2 5257.1 6089.2 5301 5012.2 4799.1 4663.3 4899.2 4935 4934.9 5040.8 5495.2 5846.6 5909 6850.4 6642 6001.9 5796.7 5774.6 6175.6 6057.8 6012.2 6077.4 6553.6 6997.7 6821.7 7499.2 7488 7013.7 6685.8 6672.5 7157.5 7026 6998.2 7116.6 7668.4 8263 8104.7 9015.3 9077 8354.7 8123.2 8142 8703.5 8642 8628.8 8767.7 9446.5 10082.7 9790.8 10728.5 10757 9323.8 9317.6 9343.2 10028.4 9941.6 9936.5 10115.6 10912.8 11717.6 11339 12610

12718 12334.2 11321.7 11510.4 12455.1 12329.9 12252.8 12569.8 13536.5 14284.8 13910.9 15329.5 15249 13769.1 13588 13649 14696.8 14565.1 14408 14705 15865.1 16546.4 16128.9 17739.7 ;

proc gplot; plot dif1*t;

symbol v=star c=blue i=join; run;

对系列进行平稳性、纯随机性检验

data e5_12; input x@@; dif1=dif(x); dif1_12=dif12(dif1); t=_n_; cards;

3333 3047.1 2876.1 2820.9 2929.6 2908.7 2851.4 3065.7 3136.9 3347.3 3421.7 4033.3 3552 3416 3197.4 3163.3 3320.5 3302.8 3244.2 3284.4 3627.2 3815.2 3831.1 4270.2

3907 3706.4 3494.8 3406.9 3463.3 3576.9 3562.1 3609.6 3971.8 4204.4 4202.7 4735.7 4753 4328.3 4213.4 4156.2 4343.3 4371.1 4378.8 4480.7 4876 5183.2 5257.1 6089.2 5301 5012.2 4799.1 4663.3 4899.2 4935 4934.9 5040.8 5495.2 5846.6 5909 6850.4 6642 6001.9 5796.7 5774.6 6175.6 6057.8 6012.2 6077.4 6553.6 6997.7 6821.7 7499.2 7488 7013.7 6685.8 6672.5 7157.5 7026 6998.2 7116.6 7668.4 8263 8104.7 9015.3 9077 8354.7 8123.2 8142 8703.5 8642 8628.8 8767.7 9446.5 10082.7 9790.8 10728.5 10757 9323.8 9317.6 9343.2 10028.4 9941.6 9936.5 10115.6 10912.8 11717.6 11339 12610

12718 12334.2 11321.7 11510.4 12455.1 12329.9 12252.8 12569.8 13536.5 14284.8 13910.9 15329.5 15249 13769.1 13588 13649 14696.8 14565.1 14408 14705 15865.1 16546.4 16128.9 17739.7 ;

proc gplot; plot dif1_12*t;

symbol v=star c=blue i=join; proc arima;

identify var=dif1_12;

identify var= dif1_12 minic p=(0:5) q=(0:5); estimate q=1;

17

forecast lead=5; run;

data e5_12; input x@@; dif1=dif(x);

dif1_12=dif12(dif1); t=_n_; cards;

3333 3047.1 2876.1 2820.9 2929.6 2908.7 2851.4 3065.7 3136.9 3347.3 3421.7

4033.3 3552 3416 3197.4 3163.3 3320.5 3302.8 3244.2 3284.4 3627.2 3815.2 3831.1 4270.2

3907 3706.4 3494.8 3406.9 3463.3 3576.9 3562.1 3609.6 3971.8 4204.4 4202.7 4735.7

4753 4328.3 4213.4 4156.2 4343.3 4371.1 4378.8 4480.7 4876 5183.2 5257.1 6089.2 5301 5012.2 4799.1 4663.3 4899.2 4935 4934.9 5040.8 5495.2 5846.6 5909 6850.4 6642 6001.9 5796.7 5774.6 6175.6 6057.8 6012.2 6077.4 6553.6 6997.7 6821.7 7499.2

7488 7013.7 6685.8 6672.5 7157.5 7026 6998.2 7116.6 7668.4 8263 8104.7 9015.3 9077 8354.7 8123.2 8142 8703.5 8642 8628.8 8767.7 9446.5 10082.7 9790.8 10728.5

10757 9323.8 9317.6 9343.2 10028.4 9941.6 9936.5 10115.6 10912.8 11717.6 11339 12610

12718 12334.2 11321.7 11510.4 12455.1 12329.9 12252.8 12569.8 13536.5 14284.8 13910.9 15329.5

15249 13769.1 13588 13649 14696.8 14565.1 14408 14705 15865.1 16546.4 16128.9 17739.7 ;

proc gplot; plot dif1_12*t;

symbol v=star c=blue i=join; proc arima;

identify var=dif1_12; estimate q=1 noint; forecast lead=5 id=time ; run;

18