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 
## 2.36133 8.48324 2.91260 0.02295 0.13503 0.30739

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## 第 2 折交叉验证

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## 误差
##     mae     mse    rmse    mape    nmse    nmae 
## 1.66956 3.92194 1.98039 0.01606 0.07137 0.22774

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## 第 3 折交叉验证

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## 误差
##     mae     mse    rmse    mape    nmse    nmae 
## 0.76381 0.92189 0.96015 0.00711 0.03765 0.16239

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## 第 4 折交叉验证

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## 误差
##      mae      mse     rmse     mape     nmse     nmae 
##  2.76335 10.15485  3.18667  0.02461  0.78316  0.90718

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## 第 5 折交叉验证

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## 误差
##     mae     mse    rmse    mape    nmse    nmae 
## 1.10329 2.25009 1.50003 0.00949 0.04930 0.16447

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## 第 6 折交叉验证

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## 误差
##      mae      mse     rmse     mape     nmse     nmae 
##  5.40967 32.71960  5.72010  0.04528  0.31529  0.53360

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 
## 0.394694 0.265793 0.515552 0.003585 0.007391 0.071289

预测

外推预测 

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误差
     mae      mse     rmse     mape     nmse     nmae 
 4.96240 25.16884  5.01686  0.04081  0.21227  0.45575 
外推预测 

plot of chunk unnamed-chunk-8plot of chunk unnamed-chunk-8 ## 总体误差

              mae     mse   rmse     mape     nmse    nmae
第 1 折    2.3613  8.4832 2.9126 0.022950 0.135033 0.30739
第 2 折    1.6696  3.9219 1.9804 0.016055 0.071374 0.22774
第 3 折    0.7638  0.9219 0.9602 0.007110 0.037647 0.16239
第 4 折    2.7634 10.1548 3.1867 0.024611 0.783158 0.90718
第 5 折    1.1033  2.2501 1.5000 0.009490 0.049299 0.16447
第 6 折    5.4097 32.7196 5.7201 0.045283 0.315291 0.53360
测试集总体 2.3452  9.7419 3.1212 0.020917 0.270912 0.42358
训练集总体 0.3947  0.2658 0.5156 0.003585 0.007391 0.07129
外推预测   4.9624 25.1688 5.0169 0.040811 0.212275 0.45575

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  102.3      106.4 1.453513 1.453513    1.441e-02
2  2007-08-01 102.4  103.2      106.4 0.732938 0.732938    7.155e-03
3  2007-09-01 102.6  102.9      106.3 0.352171 0.352171    3.434e-03
4  2007-10-01 103.1  103.2      106.6 0.068656 0.068656    6.657e-04
5  2007-11-01 103.4  103.8      106.3 0.411583 0.411583    3.981e-03
6  2007-12-01 103.9  104.5      106.7 0.572280 0.572280    5.508e-03
7  2008-01-01 104.7  104.8      106.7 0.074820 0.074820    7.143e-04
8  2008-04-01 106.8  106.1      106.3 0.616866 0.616866    5.778e-03
9  2008-05-01 106.2  106.3      106.7 0.048174 0.048174    4.534e-04
10 2008-06-01 106.4  106.0      106.2 0.364395 0.364395    3.425e-03
11 2008-07-01 106.9  106.6      106.4 0.382841 0.382841    3.580e-03
12 2008-08-01 106.4  106.2      105.8 0.264124 0.264124    2.482e-03
13 2008-09-01 106.5  106.3      106.0 0.170995 0.170995    1.606e-03
14 2008-10-01 105.8  105.7      105.5 0.116662 0.116662    1.103e-03
15 2008-11-01 104.2  104.9      106.3 0.633865 0.633865    6.082e-03
16 2008-12-01 103.5  104.0      106.7 0.502945 0.502945    4.860e-03
17 2009-02-01 104.3  104.6      106.4 0.286424 0.286424    2.746e-03
18 2009-04-01 104.2  104.1      105.9 0.133865 0.133865    1.285e-03
19 2009-05-01 103.5  103.7      105.7 0.222748 0.222748    2.152e-03
20 2009-06-01 103.4  103.9      106.2 0.487915 0.487915    4.718e-03
21 2009-07-01 103.8  104.6      106.7 0.719774 0.719774    6.932e-03
22 2009-08-01 104.9  104.6      105.0 0.392481 0.392481    3.740e-03
23 2009-09-01 105.1  105.1      105.0 0.037472 0.037472    3.566e-04
24 2009-10-01 104.9  105.1      104.9 0.208528 0.208528    1.989e-03
25 2009-11-01 104.5  105.1      104.9 0.610205 0.610205    5.837e-03
26 2009-12-01 105.4  105.8      106.2 0.323767 0.323767    3.071e-03
27 2010-01-01 106.1  106.0      105.3 0.046579 0.046579    4.390e-04
28 2010-04-01 108.1  107.5      107.0 0.600142 0.600142    5.554e-03
29 2010-05-01 107.8  107.4      106.2 0.439108 0.439108    4.072e-03
30 2010-06-01 107.4  107.4      106.5 0.003442 0.003442    3.207e-05
31 2010-07-01 108.1  107.9      107.2 0.164487 0.164487    1.522e-03
32 2010-08-01 108.5  108.0      106.6 0.541962 0.541962    4.994e-03
33 2010-09-01 108.8  109.2      108.9 0.361602 0.361602    3.322e-03
34 2010-10-01 109.3  109.8      111.1 0.512616 0.512616    4.692e-03
35 2010-11-01 110.3  112.0      115.7 1.757760 1.757760    1.594e-02
36 2010-12-01 110.6  111.3      115.7 0.646069 0.646069    5.841e-03
37 2011-01-01 111.5  111.8      115.0 0.332651 0.332651    2.983e-03
38 2011-04-01 113.7  113.6      116.0 0.021653 0.021653    1.905e-04
39 2011-05-01 113.5  114.6      117.8 1.025131 1.025131    9.028e-03
40 2011-06-01 114.2  114.5      117.5 0.248549 0.248549    2.176e-03
41 2011-07-01 114.9  114.7      116.8 0.154323 0.154323    1.343e-03
42 2011-08-01 115.2  114.9      116.8 0.326221 0.326221    2.831e-03
43 2011-09-01 115.6  115.2      116.1 0.407140 0.407140    3.522e-03
44 2011-10-01 115.3  115.4      116.1 0.077784 0.077784    6.748e-04
45 2011-11-01 114.7  115.0      115.8 0.290928 0.290928    2.537e-03
46 2011-12-01 114.9  114.5      114.2 0.466612 0.466612    4.060e-03
47 2012-03-01 116.8  116.8      116.6 0.065578 0.065578    5.612e-04
48 2012-04-01 117.0  116.8      116.8 0.135463 0.135463    1.158e-03
49 2012-05-01 116.5  115.8      114.4 0.684655 0.684655    5.877e-03
50 2012-06-01 115.7  115.6      114.2 0.143420 0.143420    1.240e-03
51 2012-07-01 116.3  115.1      114.0 1.177595 1.177595    1.013e-02
52 2012-08-01 117.0  116.7      113.7 0.270539 0.270539    2.313e-03
53 2012-09-01 117.2  117.0      116.9 0.178055 0.178055    1.519e-03
54 2012-10-01 116.7  116.8      116.6 0.148301 0.148301    1.271e-03
55 2012-11-01 116.5  116.6      117.0 0.113219 0.113219    9.716e-04
56 2012-12-01 117.1  116.9      115.6 0.173356 0.173356    1.480e-03
57 2013-01-01 118.3  117.8      115.9 0.432424 0.432424    3.656e-03
58 2013-04-01 119.0  118.5      114.7 0.469147 0.469147    3.944e-03
59 2013-05-01 118.5  118.6      113.1 0.151989 0.151989    1.283e-03
60 2013-06-01 118.6  118.7      113.3 0.103682 0.103682    8.742e-04
61 2013-07-01 119.0  118.8      112.9 0.189836 0.189836    1.596e-03
62 2013-08-01 119.3  119.1      113.4 0.188693 0.188693    1.582e-03
63 2013-09-01 120.1  119.7      113.0 0.473777 0.473777    3.943e-03
64 2013-10-01 120.5  119.6      113.3 0.873314 0.873314    7.247e-03
65 2013-11-01 120.0  119.4      112.9 0.667130 0.667130    5.558e-03
66 2013-12-01 120.4  119.6      113.3 0.794864 0.794864    6.603e-03
67 2014-01-01 121.6  117.7      117.7 3.887016 3.887016    3.197e-02
68 2014-04-01 121.7  117.0      117.0 4.689731 4.689731    3.854e-02
69 2014-05-01 121.7  116.2      116.2 5.505749 5.505749    4.525e-02
70 2014-06-01 121.4  115.7      115.7 5.767115 5.767115    4.749e-02
   预测相对误差
1     1.441e-02
2     7.155e-03
3     3.434e-03
4     6.657e-04
5     3.981e-03
6     5.508e-03
7     7.143e-04
8     5.778e-03
9     4.534e-04
10    3.425e-03
11    3.580e-03
12    2.482e-03
13    1.606e-03
14    1.103e-03
15    6.082e-03
16    4.860e-03
17    2.746e-03
18    1.285e-03
19    2.152e-03
20    4.718e-03
21    6.932e-03
22    3.740e-03
23    3.566e-04
24    1.989e-03
25    5.837e-03
26    3.071e-03
27    4.390e-04
28    5.554e-03
29    4.072e-03
30    3.207e-05
31    1.522e-03
32    4.994e-03
33    3.322e-03
34    4.692e-03
35    1.594e-02
36    5.841e-03
37    2.983e-03
38    1.905e-04
39    9.028e-03
40    2.176e-03
41    1.343e-03
42    2.831e-03
43    3.522e-03
44    6.748e-04
45    2.537e-03
46    4.060e-03
47    5.612e-04
48    1.158e-03
49    5.877e-03
50    1.240e-03
51    1.013e-02
52    2.313e-03
53    1.519e-03
54    1.271e-03
55    9.716e-04
56    1.480e-03
57    3.656e-03
58    3.944e-03
59    1.283e-03
60    8.742e-04
61    1.596e-03
62    1.582e-03
63    3.943e-03
64    7.247e-03
65    5.558e-03
66    6.603e-03
67    3.197e-02
68    3.854e-02
69    4.525e-02
70    4.749e-02