4.3.1 Accuracy assessment

Regarding how to select the appropriate accuracy evaluation criteria, Yokuma and Armstrong [33] have done a survey of expert opinions. They think that accuracy, clear physical meaning, and being easy to implement can be the critical evaluation criteria [33]. Accordingly, three criteria are used to evaluate the accuracy of the prediction model.


#### Table 6.

Three criteria to evaluate the accuracy of models.

Beijing (1990–2016) and Chongqing (1990–2015). The divided states involved in the GMM are shown in Table 7, and the transition matrixes of GMM associated with Beijing and Chongqing are denoted as P<sup>2</sup> and P3. For simplification, we only list the form of transition matrix P2. The comparison of GM(1,1) and GMM can be seen in Tables 8 and 9. The average relative errors of GM(1,1) and GMM of Beijing (Chongqing) are 0.0312 (0.5285) and 0.0029 (0.1051), respectively. The Gray

Using Gray-Markov Model and Time Series Model to Predict Foreign Direct Investment Trend…

Area Error state E1 E2 E3 E4 E5 Beijing Range [0.47, 0.2] [0.2, 0.1] [0.1, 0.1] [0.1, 0.28] [0.28, 0.65] Chongqing Range [0, 0.28] [0.28, 0.55] [0.55, 0.75] [0.75, 0.81] [0.81,0.97]

Year Original value GM(1,1) GMM TSM To state GR MR 27,696 0.0277 0.0277 0.0277 E3 0 0 24,482 0.0693 0.0371 0.0245 E5 0.6466 0.3395 34,984 0.0780 0.0417 0.0364 E5 0.5514 0.1614 66,693 0.0878 0.0711 0.0311 E4 0.2401 0.0618 144,460 0.0988 0.1121 0.0863 E1 0.4625 0.2885 140,277 0.1112 0.1262 0.1342 E1 0.2617 0.1117 155,290 0.1251 0.1420 0.1969 E1 0.2410 0.0934 159,286 0.1408 0.1620 0.1514 E2 0.1310 0.0165 216,800 0.1585 0.1799 0.2127 E1 0.3677 0.2050 197,525 0.1784 0.2052 0.2126 E2 0.1071 0.0373 168,368 0.2008 0.1626 0.2680 E4 0.1615 0.0352 176,818 0.2260 0.1831 0.1767 E4 0.2176 0.0341 172,464 0.2544 0.1361 0.2213 E5 0.3220 0.2673 219,126 0.2863 0.2319 0.1890 E4 0.2346 0.0551 255,974 0.3222 0.2610 0.2560 E4 0.2056 0.0193 352,834 0.3627 0.3627 0.2878 E3 0.0271 0.0271 455,191 0.4082 0.4694 0.3979 E2 0.1151 0.0303 506,572 0.4594 0.5283 0.5179 E2 0.1026 0.0412 608,172 0.5171 0.5947 0.5870 E2 0.1761 0.0227 612,094 0.5820 0.5820 0.6851 E3 0.0517 0.0517 636,358 0.6550 0.6550 0.7277 E3 0.0285 0.0285 705,447 0.7373 0.8368 0.7195 E5 0.0431 0.1570 804,160 0.8298 0.6721 0.8222 E4 0.0309 0.1964 852,418 0.9339 0.7565 0.9097 E4 0.0873 0.1268 904,085 1.0512 1.0512 1.0009 E3 0.1399 0.1399 1,299,635 1.1831 1.3428 1.0292 E1 0.0985 0.0322 1,302,858 1.3316 1.5114 1.4400 E1 0.0216 0.1380 Annotations: In Table 8, the unit of original value is 1 million dollars. GM, GMM, and TSM represent the predicted value of Gray model, Gray-Markov model, and time series model, and their unit is 106 million dollars. GR and MR represent the residuals of Gray model and Gray-Markov model. Data source: Beijing Statistical Yearbook (1990–2017), Beijing Municipal Bureau of Statistics.

Table 7.

Table 8.

111

Comparison of predicted errors of GMM and GM(1,1) of Beijing FDI level.

Residual states of FDI in Beijing and Chongqing.

DOI: http://dx.doi.org/10.5772/intechopen.83801

Figure 3. Original value and that in GMM.

Figure 4. Original value and that in TSM.

## 4.3.2 Comparing predicted values with actual values

As shown in Table 6, the prediction accuracy of GMM has been improved manifestly compared with that in GM(1,1) model. Therefore, the forecasting value in GMM is closer to the actual level of China's FDI. Then, from Figures 3 and 4, we can clearly see that GMM model has a better fitting effect than that in TSM.
