5. Empirical analysis of FDI in Chongqing and Beijing

From discussions above, it is found that GMM has higher prediction accuracy and better fitting effects than those of TSM of Chinese FDI level. To further verify the credibility of this result, we construct GMM and TSM based on the FDI level of Using Gray-Markov Model and Time Series Model to Predict Foreign Direct Investment Trend… DOI: http://dx.doi.org/10.5772/intechopen.83801

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


Table 7.

Residual states of FDI in Beijing and Chongqing.


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 8.

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

4.3.2 Comparing predicted values with actual values

Figure 3.

Figure 4.

110

Original value and that in TSM.

Original value and that in GMM.

Time Series Analysis - Data, Methods, and Applications

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

From discussions above, it is found that GMM has higher prediction accuracy and better fitting effects than those of TSM of Chinese FDI level. To further verify the credibility of this result, we construct GMM and TSM based on the FDI level of

can clearly see that GMM model has a better fitting effect than that in TSM.

5. Empirical analysis of FDI in Chongqing and Beijing

relational degrees of GM(1,1) and GMM of Beijing (Chongqing) are 64.62% (75.26%) and 79.39% (86.82%), respectively. Therefore, the errors of GM(1,1) and GMM are barely qualified or qualified, and hence GMM is superior to GM(1,1):


Similar to Section 4.2, TSM of Beijing FDI can be modeled as MA (1):

Year Original value GM(1,1) GMM TSM To state GR MR 2009 401,643 4.1914 3.6046 0.6941 E1 0.0417 �0.1143 2010 304,264 4.8388 2.8307 0.6809 E2 0.3712 �0.0749 2011 582,575 5.5862 3.2679 0.2878 E2 �0.0429 �0.7827 2012 352,418 6.4490 3.7727 1.2269 E2 0.4535 0.0659 2013 414,353 7.4452 4.3554 0.2769 E2 0.4435 0.0487 2014 423,348 8.5952 1.8909 0.5837 E4 0.5075 �1.2388 2015 377,183 9.9228 2.1830 0.5124 E4 0.6199 �0.7278 332 0.0033 0.0029 0.0003 E1 0 �0.1628 Annotations: In Table 9, 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 10<sup>5</sup> million dollars. GR and MR represent the residuals of Gray Model and Gray-Markov model. Data source: Chongqing Statistical Yearbook

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

TSM of Chongqing FDI can be modeled as ARMA(1,2,1):

Original value and that in GMM of BJ. Annotations: BJ denotes the city of Beijing.

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

where X ¼ num � 0:27264 and t ¼ year.

(1990–2016), Beijing Municipal Bureau of Statistics.

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

Table 9.

Figure 5.

where X ¼ num � 2:178452 and t ¼ year.

ð Þ <sup>1</sup> <sup>þ</sup> <sup>0</sup>:82673B <sup>1</sup> � B2 Xt <sup>¼</sup> <sup>ε</sup><sup>t</sup>

ð Þ <sup>1</sup> � <sup>0</sup>:82442B ð Þ <sup>1</sup> <sup>þ</sup> <sup>B</sup> <sup>1</sup> � <sup>B</sup><sup>2</sup> Xt <sup>¼</sup> <sup>ε</sup><sup>t</sup>

Figure 5 (Figure 6) shows the difference between the original value and the predicting value in Gray-Markov model (time series model) of foreign direct investment in Beijing. It is apparent that the fitting effect of GMM is better than


Using Gray-Markov Model and Time Series Model to Predict Foreign Direct Investment Trend… DOI: http://dx.doi.org/10.5772/intechopen.83801


Annotations: In Table 9, 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 10<sup>5</sup> million dollars. GR and MR represent the residuals of Gray Model and Gray-Markov model. Data source: Chongqing Statistical Yearbook (1990–2016), Beijing Municipal Bureau of Statistics.

#### Table 9.

relational degrees of GM(1,1) and GMM of Beijing (Chongqing) are 64.62% (75.26%) and 79.39% (86.82%), respectively. Therefore, the errors of GM(1,1) and GMM are barely qualified or qualified, and hence GMM is superior to GM(1,1):

> 

 

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CCCCCCCCCCCCCCA , Pð Þ<sup>5</sup> ¼

Year Original value GM(1,1) GMM TSM To state GR MR 332 0.0033 0.0029 0.0003 E1 0 �0.1628 977 0.3159 0.0347 0.0010 E5 0.9691 0.7188 1992 10,247 0.3647 0.1276 0.0029 E3 0.7190 0.1972 1993 25,915 0.4210 0.2463 0.0846 E2 0.3844 �0.0523 1994 44,953 0.4860 0.4180 0.0686 E1 0.0751 �0.0755 1995 37,926 0.5611 0.3282 0.0842 E2 0.3241 �0.1554 1996 21,878 0.6478 0.2267 0.0406 E3 0.6623 0.0350 1997 38,466 0.7478 0.4375 0.0165 E2 0.4856 0.1207 1998 43,107 0.8633 0.5050 0.0755 E2 0.5007 0.1465 1999 23,893 0.9967 0.2193 0.0563 E4 0.7603 �0.0897 2000 24,436 1.1506 0.2531 0.0181 E4 0.7876 0.0347 2001 25,649 1.3284 0.2922 0.0296 E4 0.8069 0.1223 2002 28,089 1.5335 0.1687 0.0329 E5 0.8168 �0.6651 2003 31,112 1.7704 0.1947 0.0360 E5 0.8243 �0.5976 2004 40,508 2.0439 0.4497 0.0417 E4 0.8018 0.0991 2005 51,575 2.3596 0.5191 0.0599 E4 0.7814 0.0065 2006 69,595 2.7241 0.9534 0.0776 E3 0.7445 0.2700 2007 108,534 3.1448 1.1007 0.1059 E3 0.6549 0.0139 2008 272,913 3.6306 3.1223 0.1930 E1 0.2483 0.1259

 

   

 

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 <sup>0</sup>

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 <sup>0</sup>

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Pð Þ<sup>1</sup> ¼

 

 

 

BBBBBBBBBBBBBB@

 

 

   

 <sup>0</sup>

<sup>2</sup>

Pð Þ <sup>4</sup> ¼

 

 

  CCCCCCCCCCCCCCA , Pð Þ<sup>2</sup> ¼

Time Series Analysis - Data, Methods, and Applications

 

 

 

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

Similar to Section 4.2, TSM of Beijing FDI can be modeled as MA (1):

$$(\mathbf{1} + \mathbf{0}.\mathbf{82673B}) \left(\mathbf{1} - \mathbf{B}^2\right) \mathbf{X}\_\mathbf{t} = \mathbf{e}\_\mathbf{t}$$

where X ¼ num � 0:27264 and t ¼ year. TSM of Chongqing FDI can be modeled as ARMA(1,2,1):

$$(\mathbf{1} - \mathbf{0}.\mathbf{82}\mathbf{44}\mathbf{2B})(\mathbf{1} + \mathbf{B})(\mathbf{1} - \mathbf{B}^2)\mathbf{X}\_\mathbf{t} = \mathbf{e}\_\mathbf{t}$$

where X ¼ num � 2:178452 and t ¼ year.

Figure 5 (Figure 6) shows the difference between the original value and the predicting value in Gray-Markov model (time series model) of foreign direct investment in Beijing. It is apparent that the fitting effect of GMM is better than

Figure 5. Original value and that in GMM of BJ. Annotations: BJ denotes the city of Beijing.

Figure 6. Original value and that in TSM of BJ. Annotations: BJ denotes the city of Beijing.

that of TSM. The similar conclusion can be drawn from Figures 7 and 8. Tables 9 and 10 show the predicting effect of GMM is better than that of TSM from the point of predicting errors and accuracy. There is no doubt that it is a good thing to predict accurately the foreign direct investment of the forthcoming 5 or 10 years for the domain specialists. Because if the predicting results is lower or higher than they expected, they could pay attention to seeking the critical factors and policy which have impacts on FDI and adjust them in advance.

6. Conclusions and future work

Comparison of predicting accuracy of two models.

Area Index MSE <sup>¼</sup> <sup>1</sup>

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

Figure 8.

error.

115

Table 10.

international investment.

Our contributions are threefold. Firstly, comparing the predicting results of the Gray-Markov model and the time series model and the original value, respectively, we can find that the fitting effect of the former (GMM) is better than the latter (TSM) and so does its scientific and practical importance. Secondly, the predicting results of GMM show that the level of foreign investment in China has been increasing by years. Thirdly, in order to further enhance Chinese international status and attract more foreign investment, the government should play a role at a macro level to reduce excessive market administrative intervention, establish a service-oriented government, and reduce the relevant approval procedures for

Original value and that in TSM of CQ. Annotations: CQ denotes the city of Chongqing.

<sup>n</sup> <sup>∑</sup><sup>n</sup>

<sup>i</sup>¼<sup>1</sup> xi � <sup>b</sup>xi ð Þ<sup>2</sup> MAE <sup>¼</sup> <sup>1</sup>

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

GMM 4.3599e+09 3.9369e+04 0.1032 TSM 5.4378e+09 4.6731e+04 0.1335

GMM 5.8230e+09 3.4080e+04 0.2663 TSM 4.4524e+10 1.0126e+05 0.6018 Annotations: MSE, MAE, and MAPE denote mean squared error, mean absolute error, and mean absolute percentage

Beijing GM(1,1) 3.3244e+09 4.7473e+04 0.2587

Chongqing GM(1,1) 3.9173e+10 1.3478e+05 2.9584

<sup>n</sup> <sup>∑</sup><sup>n</sup>

<sup>i</sup>¼<sup>1</sup> xi � <sup>x</sup>b<sup>i</sup> j j MAPE <sup>¼</sup> <sup>1</sup>

<sup>n</sup> <sup>∑</sup><sup>n</sup> i¼1 xi�bxi xi � � � � � �

Figure 7. Original value and that in GMM of CQ. Annotations: CQ denotes the city of Chongqing.

Using Gray-Markov Model and Time Series Model to Predict Foreign Direct Investment Trend… DOI: http://dx.doi.org/10.5772/intechopen.83801

Figure 8. Original value and that in TSM of CQ. Annotations: CQ denotes the city of Chongqing.


Annotations: MSE, MAE, and MAPE denote mean squared error, mean absolute error, and mean absolute percentage error.

#### Table 10.

that of TSM. The similar conclusion can be drawn from Figures 7 and 8. Tables 9 and 10 show the predicting effect of GMM is better than that of TSM from the point of predicting errors and accuracy. There is no doubt that it is a good thing to predict accurately the foreign direct investment of the forthcoming 5 or 10 years for the domain specialists. Because if the predicting results is lower or higher than they expected, they could pay attention to seeking the critical factors

Original value and that in TSM of BJ. Annotations: BJ denotes the city of Beijing.

Time Series Analysis - Data, Methods, and Applications

Figure 6.

Figure 7.

114

and policy which have impacts on FDI and adjust them in advance.

Original value and that in GMM of CQ. Annotations: CQ denotes the city of Chongqing.

Comparison of predicting accuracy of two models.
