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

liquidity and has a promoting effect on FDI mobility [10]. Badr and Ayed do a quantitative study of the relationship between FDI and economic development in South American countries, and they find that FDI can be determined by some economic factors, having no important effect on economic development [11]. Kathuria et al. apply panel data to examining the effectiveness of public policy in attracting FDI [12]. Lin et al. divide the FDI company into five strategies [13]; Brülhat and Schmidheiny estimate the rivalness of state-level inward FDI [14].

The trend of FDI in the future is an important reference for China's economic development. However, much literature focuses on the development of FDI itself and its influencing factors, and there is little research on the future development. This is what we do in this chapter. Currently, the predictive analysis model for economic and trade development can be divided into linear prediction method and nonlinear prediction one. The linear prediction method mainly includes historical average level prediction method, time series prediction method, and Kalman filter prediction method, to name just a few. The nonlinear prediction methods concern Gray theory, Markov chain, support vector machine, and boom prediction method. The historical average prediction algorithm is simple and easy to understand and the parameters can be estimated by using the least squares method. However, it is too simple to accurately reflect the randomness and nonlinearity, and therefore it cannot be applied to unexpected events. The Kalman filter uses the flexible recursive state space model, with the advantages of linear, unbiased, and minimum mean variance. Nevertheless, because the Kalman filter prediction model belongs to the linear model, its performance becomes worse in the nonlinearity and uncertainty [15]. The time series model is simple in modeling, with high prediction accuracy in the case of full historical data. The Gray model can be modeled with less information, handling data easily and having higher accuracy, which can be extensively used in several fields [15–18]. However, Gray model becomes less attractive for time series with large stochastic fluctuation. Markov stochastic process predicts the development and changes of dynamic system according to the transfer probability of different states, and the transfer probability reflects the influence degrees of various stochastic factors and the internal law of the transition states. Therefore, it is more suitable to predict the problems with large stochastic fluctuation. What cannot be ignored is that Markov model requires data to meet the characteristics of no effect. Consequently, when using a simple model, it is very difficult to obtain a better prediction result, and the combination method becomes a popular method.

Through the vector autoregressive moving average (VARMA), Bhattacharya et al. compare and analyze the consumer price index sequence (CPI) and improve the forecasting accuracy [16]. The Gray model (proposed by a Chinese scholar, Professor Deng) and the Markov model (proposed by a Russian mathematician, Markov) have been combined very early, which is called Gray-Markov model (GMM). Based on the Gray prediction model, GMM is used to solve the inaccurate problems resulting from the large random fluctuation of the data and widely promoted in the fields of financial economy, agricultural economy, and resource and energy [17–20]. On the basis of GM(1,1), Li et al. propose an improved GM(2,1) model [21]. Based on the model of GM(1,1) and Markov stochastic process and combining Taylor formula approximation method, Li et al. construct a model of T-MC-RGM(1,1) and verify its validity by the example of thermal power station in Japan [22].

The level of FDI in China is influenced by many factors such as fixed investment, laws and regulations, corporate culture, innovation ability, and financial market stability, among others. To clearly recognize and describe the role of FDI, the foreign investment system is abstracted as a Gray system with no physical prototype and incomplete information, which can be predicted with GM(1,1)

Therefore, it is necessary to focus on the future tendency of FDI in the supply chain system when we investigate the transformation and innovation of Chinese

Time Series Analysis - Data, Methods, and Applications

Since the late 1970s, FDI attracted by China has been steadily increasing, regardless of the changes and fluctuation of the international economic environment and the total flow of FDI globally. Statistically, over the period from 1979 to 2010, China's actual use of FDI amounted to \$1048.31 billion [2], and FDI keeps a rapid growth. According to the data of Ministry of Commerce of the People's Republic of China (PRC) (Figure 1), the FDI in China presented a rising trend over the period from 1990 to 2016. The vital roles in the economic development of China are as follows. Firstly, the proportion of basic industries in China declines generally, and the proportion of agricultural output drops by 18% over the period between 1978 and 2011 [3]. Secondly, for a long time, FDI mainly concentrates in secondary and tertiary industries, accelerating the restructuring and upgrading of China's industries [4]. Finally, FDI provides investment capital and promotes the rapid development of China's import and export trade, improving China's status in

Due to the remarkable role of FDI, a multitude of scholars began to track and study the FDI in developing countries, build analytical framework, and launch a new field of research of FDI in developing countries. The statistics shows that China has become an emerging market for FDI. Dees indicates that FDI has positive effects on the GDP, technological progress, and the improvement of management system [5]. Nourzad considers that FDI promotes economy development through technology transfer [6], while Mah argues that the latter one promotes the former one [7]. Taking the reform policy (implemented in July 2005) as the boundary, Pan and Song explore the impact of the effective exchange rate of RMB on FDI [8]. Research shows that they are in a long-term equilibrium relationship before implementing reform policy. After the policy, the exchange rate of RMB has the Granger causality for FDI, and the appreciation of RMB can promote the flow of FDI. Additionally, De Mello shows that FDI can increase the added value associated with it [9]. Based on the data from 1971 to 2012, Dreher et al. conclude that the membership in international organizations is an essential and decisive factor of FDI

economy.

international trade.

Figure 1.

100

The horizontal curve of FDI in China.

model. Meanwhile, the FDI level in the previous year has no direct influence on that in the next year, in line with the no-effect characteristic of Markov stochastic process. On the basis of the previous study of Gray-Markov model, it is used to predict the tendency of FDI in China, addressing the shortcomings of the Gray model for the low precision of the data sample with large fluctuation and compensating for the limitation that the Markov model requires the data to have a smooth process. As a comparison, the time series prediction model is introduced to evaluate FDI. Then, the fitting results are compared to decide the optimal prediction model.

<sup>Φ</sup>^ <sup>¼</sup> <sup>a</sup>^ ^ b � �

�Zð Þ<sup>1</sup> ð Þ<sup>2</sup> <sup>1</sup>

1

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

1

CCCCCCA , Y ¼

⋮

By differentiating <sup>x</sup>ð Þ<sup>1</sup> ð Þ<sup>k</sup> , a whitened differential equation can be written as

!

Reducing the sequence of <sup>x</sup>^ð Þ<sup>1</sup> ð Þ <sup>k</sup> <sup>þ</sup> <sup>1</sup> ð Þ <sup>k</sup> <sup>¼</sup> <sup>1</sup>; <sup>2</sup>; …; <sup>m</sup> � <sup>1</sup> , the following sequence

<sup>X</sup>^ ð Þ <sup>0</sup> <sup>¼</sup> <sup>x</sup>^ð Þ <sup>0</sup> ð Þ<sup>1</sup> ; <sup>x</sup>^ð Þ <sup>0</sup> ð Þ<sup>2</sup> ; …; <sup>x</sup>^ð Þ <sup>0</sup> ð Þ <sup>m</sup>

Model test is divided into residual test and Gray-relating test. Residual test is to obtain the difference between predicting value and the actual value. Firstly, the absolute residuals and relative residuals about <sup>X</sup>ð Þ <sup>0</sup> and <sup>X</sup>^ ð Þ <sup>0</sup> are calculated:

�Zð Þ<sup>1</sup> ð Þ<sup>3</sup>

⋮

�Zð Þ<sup>1</sup> ð Þ <sup>m</sup> <sup>1</sup>

<sup>x</sup>^ð Þ<sup>1</sup> ð Þ¼ <sup>k</sup> <sup>þ</sup> <sup>1</sup> <sup>x</sup>ð Þ<sup>1</sup> ð Þ� <sup>1</sup> ^

ϕðÞ¼ i

Then, below is the average value of relative residuals:

cient between the original sequence and the reference sequence:

<sup>Δ</sup>ð Þ <sup>0</sup> ð Þ<sup>i</sup>

<sup>Φ</sup> <sup>¼</sup> <sup>1</sup> <sup>n</sup> <sup>∑</sup> n i¼1

<sup>ε</sup>ið Þ¼ <sup>k</sup> min<sup>i</sup> min<sup>k</sup> j j x kð Þ� xið Þ<sup>k</sup> <sup>þ</sup> <sup>ρ</sup> max<sup>i</sup> max<sup>k</sup> j j x kð Þ� xið Þ<sup>k</sup>

i denotes the ith group of fitting data, and k denotes the kth one in a certain group. ρ denotes the distinguish coefficient varying from 0 to 1, which is always set as 0.5. However, the correlation coefficient varies with moments, which results in disperse information. Combining the correlation coefficient in different moments

Given the value of α, it is called residual qualification model when Φ , α. The value of α can be 0.01, 0.05, or 0.10, and the corresponding model is perfect,

As shown in Eq. (12), Gray correlation degree measures the correlating coeffi-

B ¼

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

0

BBBBBB@

(5) The whitened time response is as follows:

and

dxð Þ<sup>1</sup>

dt <sup>þ</sup> axð Þ<sup>1</sup> ð Þ¼ <sup>k</sup> <sup>b</sup>

is obtained:

(6) Model testing

qualified, and barely qualified.

103

<sup>¼</sup> BTB � ��<sup>1</sup>

BTY (5)

<sup>a</sup>^ (7)

(6)

<sup>x</sup>ð Þ <sup>0</sup> ð Þ<sup>2</sup> <sup>x</sup>ð Þ <sup>0</sup> ð Þ<sup>3</sup> ⋮ <sup>x</sup>ð Þ <sup>0</sup> ð Þ <sup>m</sup> 1

CCCCA

0

BBBB@

b a^

e

<sup>Δ</sup>ð Þ <sup>0</sup> ðÞ¼ <sup>i</sup> <sup>x</sup>^ð Þ <sup>0</sup> ðÞ�<sup>i</sup> <sup>x</sup>ð Þ <sup>0</sup> ð Þð <sup>i</sup> <sup>i</sup> <sup>¼</sup> <sup>1</sup>, <sup>2</sup>, …, n<sup>Þ</sup> (9)

j j x kð Þ� xið Þ<sup>k</sup> <sup>þ</sup> <sup>ρ</sup> max<sup>i</sup> max<sup>k</sup> j j x kð Þ� xið Þ<sup>k</sup> (12)

<sup>x</sup>^ð Þ <sup>0</sup> ð Þ<sup>i</sup> ð Þ <sup>i</sup> <sup>¼</sup> <sup>1</sup>, <sup>2</sup>, …, n (10)

ϕ<sup>i</sup> (11)

ð Þ �ak^ <sup>þ</sup> ^ b

n o (8)
