4.2 TSM predicting FDI of China

Now we will build a TSM based on the FDI value of China over the period from 1990 to 2016, obtain the predicting data, compare the difference between the predicted data and the original date, and evaluate the accuracy of this model.

Figure 1 shows the changing tendency of FDI in China over the period between 1990 and 2016. The raw data series show the seasonal change and overall growth, but the data series are not stable. Through the seasonal difference method to process the data, the seasonal difference order of three was selected. After the differential processing, the data sequence has been stabilized, eliminating the growing trend (Figure 2).

We determine the order of TSM based on sample autocorrelation function and partial autocorrelation function. After the one-step delay, the sample autocorrelation function falls to a standard error of twice times and has the property of truncation. After the two-step delay, the sample partial autocorrelation function falls to a standard error of twice times and has the property of truncation.

In the light of the calculation of SAS software, now we compare the model of ARMA(2,1), AR(2), and MA(1) (see Tables 4 and 5).

Comparing the AIC and SBC values for ARMA(2,1), AR(2), and MA(1) models (see Table 4), we find the model MA(1) to be the most inferior. Considering the AIC and SBC criterion values of ARMA(2,1) and AR(2) and the significance of parameters, it is found that fitting effect of the AR(2) model is the best.

As shown in Table 5, the P-value (Pr . ChiSq) for self-correlation test of the residual sequence with the 6-step delay, the 12-step delay and the 18-step delay are greater than that of the significant level α = 0.1. Therefore, we cannot reject the hypothesis that residuals are non-autocorrelated. That is to say, the residual is regarded as a white noise sequence. This illustrates that the AR(2) model has extracted sufficient information from the raw series and it is a rational model:

<sup>ð</sup><sup>1</sup> � <sup>1</sup>:53571<sup>B</sup> <sup>þ</sup> <sup>0</sup>:53921B<sup>2</sup>

Annotations: \*\*\*, \*\*, and \* indicate a significant level of 0.01, 0.05, and 0.1, respectively.

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

4.3 Comparison of prediction results of two models

corresponding year.

Self-correlation test of AR(2) model.

Table 4.

Table 5.

Prediction results of TSM.

4.3.1 Accuracy assessment

of the prediction model.

Index MSE <sup>¼</sup> <sup>1</sup>

Table 6.

109

<sup>n</sup> <sup>∑</sup><sup>n</sup>

Three criteria to evaluate the accuracy of models.

where X ¼ num � 2:0711, t ¼ year, and num represents the FDI value of the

To lag 6 12 18 Chi-square 3.91 5.44 8.02 Pr . ChiSq 0.4187 0.8599 0.9481

Model Parameter Estimate P-value AIC SBC AR(2) MU 2.0711 <0.0001\*\*\* 1.0603 4.5944 AR1,1 1.5357 <0.0001\*\*\* AR1,2 �0.5392 0.0102\*\* MA(1) MU 0.4676 0.0038\*\*\* 28.7297 31.08558 MA1,1 �0.7099 0.0001\*\*\* ARMA(2,1) MU 1.9380 <0.0001\*\*\* 0.7062 5.4184 MA1,1 �0.4940 0.1192 AR1,1 1.2352 0.0015\*\*\* AR1,2 �0.2358 0.5028

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

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

Criterion Mean squared error Mean absolute error Mean absolute percentage error

<sup>n</sup> <sup>∑</sup><sup>n</sup>

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

GM(1,1) 7.3991e+03 66.0812 0.3117 GMM 2.4731e+03 29.5558 0.1181 Time series 1.6644e+04 85.6101 0.1448 Annotations: x^<sup>i</sup> is the predicting value, xi is the original value, and n is the predicting number.

Þð<sup>1</sup> � <sup>B</sup><sup>3</sup>

ÞXt ¼ ε<sup>t</sup>

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

<sup>n</sup> <sup>∑</sup><sup>n</sup> i¼1 xi�x^<sup>i</sup> xi 

Figure 2. The curve about time after differential.

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


#### Table 4.

prediction accuracy of GMM has been improved, and its fitting effect exceeds the

Now we will build a TSM based on the FDI value of China over the period from

Figure 1 shows the changing tendency of FDI in China over the period between 1990 and 2016. The raw data series show the seasonal change and overall growth, but the data series are not stable. Through the seasonal difference method to process the data, the seasonal difference order of three was selected. After the differential processing, the data sequence has been stabilized, eliminating the growing trend

We determine the order of TSM based on sample autocorrelation function and partial autocorrelation function. After the one-step delay, the sample autocorrelation function falls to a standard error of twice times and has the property of truncation. After the two-step delay, the sample partial autocorrelation function falls to a standard error of twice times and has the property of truncation.

In the light of the calculation of SAS software, now we compare the model of

Comparing the AIC and SBC values for ARMA(2,1), AR(2), and MA(1) models (see Table 4), we find the model MA(1) to be the most inferior. Considering the AIC and SBC criterion values of ARMA(2,1) and AR(2) and the significance of parameters, it is found that fitting effect of the AR(2) model is the best.

As shown in Table 5, the P-value (Pr . ChiSq) for self-correlation test of the residual sequence with the 6-step delay, the 12-step delay and the 18-step delay are greater than that of the significant level α = 0.1. Therefore, we cannot reject the hypothesis that residuals are non-autocorrelated. That is to say, the residual is regarded as a white noise sequence. This illustrates that the AR(2) model has extracted sufficient information from the raw series and it is a rational model:

ARMA(2,1), AR(2), and MA(1) (see Tables 4 and 5).

1990 to 2016, obtain the predicting data, compare the difference between the predicted data and the original date, and evaluate the accuracy of this model.

model of GM(1,1).

(Figure 2).

Figure 2.

108

The curve about time after differential.

4.2 TSM predicting FDI of China

Time Series Analysis - Data, Methods, and Applications

Prediction results of TSM.


#### Table 5.

Self-correlation test of AR(2) model.

$$(\mathbf{1} - \mathbf{1}.\mathbf{53571B} + \mathbf{0}.\mathbf{53921B^2})(\mathbf{1} - B^3)\mathbf{X}\_t = \varepsilon\_t$$

where X ¼ num � 2:0711, t ¼ year, and num represents the FDI value of the corresponding year.
