分折交叉验证

## 第 1 折交叉验证

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## 误差
##     mae     mse    rmse    mape    nmse    nmae 
##  3.1444 13.5281  3.6781  0.0305  0.2153  0.4093

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## 第 2 折交叉验证

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## 误差
##     mae     mse    rmse    mape    nmse    nmae 
## 1.58255 3.53421 1.87995 0.01522 0.06432 0.21587

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## 第 3 折交叉验证

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## 误差
##     mae     mse    rmse    mape    nmse    nmae 
## 1.85162 4.61993 2.14940 0.01723 0.18867 0.39366

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## 第 4 折交叉验证

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## 误差
##      mae      mse     rmse     mape     nmse     nmae 
##  3.56907 14.85145  3.85376  0.03166  1.14537  1.17168

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## 第 5 折交叉验证

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## 误差
##     mae     mse    rmse    mape    nmse    nmae 
## 1.96116 6.14157 2.47822 0.01687 0.13456 0.29236

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## 第 6 折交叉验证

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## 误差
##      mae      mse     rmse     mape     nmse     nmae 
##  4.82470 25.65505  5.06508  0.04039  0.24722  0.47590

6折交叉验证

## 6折交叉验证

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用训练集作为测试

## 估计值与真值

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## 误差
##      mae      mse     rmse     mape     nmse     nmae 
## 0.733697 0.913496 0.955770 0.006696 0.025403 0.132519
外推预测 

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误差
     mae      mse     rmse     mape     nmse     nmae 
 7.47303 62.88085  7.92974  0.06146  0.53034  0.68633 
外推预测 

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总体误差

              mae     mse   rmse     mape    nmse   nmae
第 1 折    3.1444 13.5281 3.6781 0.030498 0.21534 0.4093
第 2 折    1.5825  3.5342 1.8799 0.015217 0.06432 0.2159
第 3 折    1.8516  4.6199 2.1494 0.017226 0.18867 0.3937
第 4 折    3.5691 14.8515 3.8538 0.031664 1.14537 1.1717
第 5 折    1.9612  6.1416 2.4782 0.016874 0.13456 0.2924
第 6 折    4.8247 25.6551 5.0651 0.040388 0.24722 0.4759
测试集总体 2.8222 11.3884 3.3747 0.025311 0.31670 0.5097
训练集总体 0.7337  0.9135 0.9558 0.006696 0.02540 0.1325
外推预测   7.4730 62.8809 7.9297 0.061461 0.53034 0.6863

拟合和预测结果

         date  真值 拟合值 分折预测值  拟合误差  预测误差 拟合相对误差
1  2007-07-01 100.9  103.8      107.5  2.953289  2.953289    2.927e-02
2  2007-08-01 102.4  103.8      107.4  1.341247  1.341247    1.309e-02
3  2007-09-01 102.6  103.8      107.4  1.266228  1.266228    1.235e-02
4  2007-10-01 103.1  104.0      107.4  0.890487  0.890487    8.634e-03
5  2007-11-01 103.4  104.4      107.4  1.030684  1.030684    9.969e-03
6  2007-12-01 103.9  105.0      107.4  1.080839  1.080839    1.040e-02
7  2008-01-01 104.7  105.0      107.4  0.273052  0.273052    2.607e-03
8  2008-04-01 106.8  105.7      105.6  1.043516  1.043516    9.774e-03
9  2008-05-01 106.2  105.8      107.4  0.399641  0.399641    3.761e-03
10 2008-06-01 106.4  105.3      107.4  1.108723  1.108723    1.042e-02
11 2008-07-01 106.9  106.2      107.4  0.702097  0.702097    6.566e-03
12 2008-08-01 106.4  106.0      105.7  0.475086  0.475086    4.464e-03
13 2008-09-01 106.5  106.3      105.8  0.157999  0.157999    1.484e-03
14 2008-10-01 105.8  105.8      105.8  0.005402  0.005402    5.106e-05
15 2008-11-01 104.2  105.4      105.8  1.218538  1.218538    1.169e-02
16 2008-12-01 103.5  104.6      106.5  1.106088  1.106088    1.069e-02
17 2009-02-01 104.3  104.8      106.5  0.525771  0.525771    5.040e-03
18 2009-04-01 104.2  104.2      106.2  0.005828  0.005828    5.593e-05
19 2009-05-01 103.5  104.1      106.1  0.586403  0.586403    5.666e-03
20 2009-06-01 103.4  104.3      106.3  0.864663  0.864663    8.361e-03
21 2009-07-01 103.8  104.6      105.4  0.742346  0.742346    7.149e-03
22 2009-08-01 104.9  104.3      104.7  0.635971  0.635971    6.060e-03
23 2009-09-01 105.1  104.8      104.0  0.260419  0.260419    2.479e-03
24 2009-10-01 104.9  104.8      104.0  0.075563  0.075563    7.206e-04
25 2009-11-01 104.5  105.2      103.9  0.634071  0.634071    6.066e-03
26 2009-12-01 105.4  106.6      105.5  1.123334  1.123334    1.065e-02
27 2010-01-01 106.1  105.9      104.1  0.202296  0.202296    1.907e-03
28 2010-04-01 108.1  106.4      104.4  1.639395  1.639395    1.517e-02
29 2010-05-01 107.8  106.6      104.3  1.248381  1.248381    1.158e-02
30 2010-06-01 107.4  106.8      105.7  0.510584  0.510584    4.756e-03
31 2010-07-01 108.1  107.3      105.9  0.797082  0.797082    7.374e-03
32 2010-08-01 108.5  107.8      106.0  0.736327  0.736327    6.785e-03
33 2010-09-01 108.8  108.0      106.6  0.884158  0.884158    8.123e-03
34 2010-10-01 109.3  108.4      110.9  0.897324  0.897324    8.212e-03
35 2010-11-01 110.3  113.1      116.2  2.809869  2.809869    2.548e-02
36 2010-12-01 110.6  110.6      116.2  0.015194  0.015194    1.374e-04
37 2011-01-01 111.5  112.9      116.0  1.440835  1.440835    1.292e-02
38 2011-04-01 113.7  113.7      116.0  0.072071  0.072071    6.340e-04
39 2011-05-01 113.5  114.7      118.4  1.130960  1.130960    9.960e-03
40 2011-06-01 114.2  114.8      118.3  0.530724  0.530724    4.646e-03
41 2011-07-01 114.9  114.6      118.2  0.308142  0.308142    2.682e-03
42 2011-08-01 115.2  114.8      118.4  0.478288  0.478288    4.150e-03
43 2011-09-01 115.6  114.7      118.0  0.857975  0.857975    7.422e-03
44 2011-10-01 115.3  115.2      116.8  0.077877  0.077877    6.756e-04
45 2011-11-01 114.7  114.9      117.0  0.254408  0.254408    2.218e-03
46 2011-12-01 114.9  114.9      116.0  0.019189  0.019189    1.670e-04
47 2012-03-01 116.8  116.8      117.7  0.035547  0.035547    3.042e-04
48 2012-04-01 117.0  116.8      117.8  0.177263  0.177263    1.515e-03
49 2012-05-01 116.5  115.9      115.3  0.618523  0.618523    5.309e-03
50 2012-06-01 115.7  116.1      112.5  0.422896  0.422896    3.655e-03
51 2012-07-01 116.3  115.0      111.7  1.284345  1.284345    1.105e-02
52 2012-08-01 117.0  116.6      112.1  0.358618  0.358618    3.066e-03
53 2012-09-01 117.2  116.8      117.5  0.430638  0.430638    3.674e-03
54 2012-10-01 116.7  116.8      117.8  0.094453  0.094453    8.097e-04
55 2012-11-01 116.5  116.8      117.8  0.228214  0.228214    1.958e-03
56 2012-12-01 117.1  117.0      115.6  0.145992  0.145992    1.247e-03
57 2013-01-01 118.3  117.3      115.6  0.942328  0.942328    7.968e-03
58 2013-04-01 119.0  118.5      114.3  0.433052  0.433052    3.640e-03
59 2013-05-01 118.5  119.0      114.3  0.524586  0.524586    4.428e-03
60 2013-06-01 118.6  119.1      114.1  0.461949  0.461949    3.895e-03
61 2013-07-01 119.0  118.7      114.0  0.267114  0.267114    2.246e-03
62 2013-08-01 119.3  119.1      114.2  0.250711  0.250711    2.101e-03
63 2013-09-01 120.1  118.7      114.1  1.410626  1.410626    1.174e-02
64 2013-10-01 120.5  118.2      114.1  2.258976  2.258976    1.875e-02
65 2013-11-01 120.0  118.9      113.3  1.076349  1.076349    8.968e-03
66 2013-12-01 120.4  118.8      114.0  1.583479  1.583479    1.315e-02
67 2014-01-01 121.6  117.8      117.8  3.810720  3.810720    3.134e-02
68 2014-04-01 121.7  115.6      115.6  6.079124  6.079124    4.995e-02
69 2014-05-01 121.7  111.7      111.7 10.019965 10.019965    8.235e-02
70 2014-06-01 121.4  111.5      111.5  9.982303  9.982303    8.220e-02
   预测相对误差
1     2.927e-02
2     1.309e-02
3     1.235e-02
4     8.634e-03
5     9.969e-03
6     1.040e-02
7     2.607e-03
8     9.774e-03
9     3.761e-03
10    1.042e-02
11    6.566e-03
12    4.464e-03
13    1.484e-03
14    5.106e-05
15    1.169e-02
16    1.069e-02
17    5.040e-03
18    5.593e-05
19    5.666e-03
20    8.361e-03
21    7.149e-03
22    6.060e-03
23    2.479e-03
24    7.206e-04
25    6.066e-03
26    1.065e-02
27    1.907e-03
28    1.517e-02
29    1.158e-02
30    4.756e-03
31    7.374e-03
32    6.785e-03
33    8.123e-03
34    8.212e-03
35    2.548e-02
36    1.374e-04
37    1.292e-02
38    6.340e-04
39    9.960e-03
40    4.646e-03
41    2.682e-03
42    4.150e-03
43    7.422e-03
44    6.756e-04
45    2.218e-03
46    1.670e-04
47    3.042e-04
48    1.515e-03
49    5.309e-03
50    3.655e-03
51    1.105e-02
52    3.066e-03
53    3.674e-03
54    8.097e-04
55    1.958e-03
56    1.247e-03
57    7.968e-03
58    3.640e-03
59    4.428e-03
60    3.895e-03
61    2.246e-03
62    2.101e-03
63    1.174e-02
64    1.875e-02
65    8.968e-03
66    1.315e-02
67    3.134e-02
68    4.995e-02
69    8.235e-02
70    8.220e-02