Computers, Materials & Continua DOI:10.32604/cmc.2021.016770 

Article 
An Adaptive Lasso Grey Model for Regional FDI Statistics Prediction
1Centre for Innovation Research in Social Governance, Changsha University of Science and Technology, Changsha, 410114, China
2College of Information Technology and Management, Hunan University of Finance and Economics, Changsha, 410205, China
3Department of Mathematics and Computer Science, Northeastern State University, Tahlequah, 74464, USA
*Corresponding Author: Huajun Huang. Email: huanghuajun@hufe.edu.cn
Received: 11 January 2021; Accepted: 26 April 2021
Abstract: To overcome the deficiency of traditional mathematical statistics methods, an adaptive Lasso grey model algorithm for regional FDI (foreign direct investment) prediction is proposed in this paper, and its validity is analyzed. Firstly, the characteristics of the FDI data in six provinces of Central China are generalized, and the mixture model's constituent variables of the Lasso grey problem as well as the grey model are defined. Next, based on the influencing factors of regional FDI statistics (mean values of regional FDI and median values of regional FDI), an adaptive Lasso grey model algorithm for regional FDI was established. Then, an application test in Central China is taken as a case study to illustrate the feasibility of the adaptive Lasso grey model algorithm in regional FDI prediction. We also select RMSE (root mean square error) and MAE (mean absolute error) to demonstrate the convergence and the validity of the algorithm. Finally, we train this proposedal gorithm according to the regional FDI statistical data in six provinces in Central China from 2006 to 2018. We then use it to predict the regional FDI statistical data from 2019 to 2023 and show its changing tendency. The extended work for the adaptive Lasso grey model algorithm and its procedure to other regional economic fields is also discussed.
Keywords: Adaptive lasso grey model algorithm; regional FDI statistics; mean value of regional FDI; median value of regional FDI
Economic development varies from country to country, and the influencing factors of the regional FDI are also varied [1–3]. The regional FDI statistics can accurately and effectively describe the relationship among basic situation, influencing factors and investment trend of regional FDI.
How to effectively predict regional FDI statistics to improve the regional economy is a complicated problem. In the past decade, many traditional statistical methods [4–7] have been proposed to solve this problem. Being empirical or semiempirical, these models can provide neither specific assumptions nor sufficent statistical data.
Lasso's method can effectively overcome the above deficiency of the traditional statistical methods. In this method,proper variables with a significant impact can be selected to reduce the complexity of data [8] and display the influence of all variables on the estimated parameters [9]. However, Lasso’s method has some defects in precision. The adaptive Lasso method [10] assigns different weights to different coefficients to improve the accuracy of calculation parameters.
In recent years, many studies have shown that the grey theory is a valid method that can correctly predict the properties in some fields [11–13] by mining some available information and extracting valuable key information. The regional FDI system is a typical grey system suitable for the grey model with both the evident hierarchy complexity and the constant change, and its index characteristic data is uncertain and incomplete [14–21]. Therefore, it is feasible to combine the adaptive Lasso method and the grey model, i.e., to establish an adaptive Lasso grey algorithm to predict regional FDI statistics.
2 Adaptive Lasso Grey Model Algorithms Predicting Regional FDI Statistics
Many methods [22,23] have been proposed to solve the Lasso problem. However, these methods can only deal with big data, not minor data problems. Therefore, the adaptive Lasso model [24] and the grey model [25–29] are needed to precisely calculate the predicted value. Based on characteristics [30,31] and the regional FDI statistics variables, the main algorithm in this paper is described as follows.
According to the data of regional FDI, let:
Adaptive Lasso Grey Model Algorithm Predicting Regional FDI Statistics:
Step 1: Investigate the possible factors of regional FDI and obtain their specific data.
Step 2: Set the value range of the variables sample matrix
Step 3: Specify the required statistics (the regional FDI data, the mean and median values influencing factors) and get the statistical matrix
Step 4: Initialize β and solve the leastsquares estimation y = Xβ, then get β.
Step 5: Compute the weight vector:
Step 6: For the adaptive Lasso model:
Step 7: Set
where
Step 8: Let
Step 9: If
Step 10: Establish the adaptive Lasso model according to
Step 11: Select
Step 12: Substitute
Step 13: Solve
Step 14: Substitute (6) into (7), get:
if
Step 15: For all
Step 16:Establish the adaptive Lassogrey model (Step10) and compute the regional FDI statistics y for future years.
Among many forms of regional FDI statistics,this paper only considers the mean and median values to illustrate the feasibility and effectiveness of our proposed algorithm.. Taking six provinces of Central China as the case for study, through numerical analysis of regional FDI, their overall regional FDI capacity is judged [32], which provides reference for formulating related policies.
In this case study , we select the data of regional FDI from 2006 to 2018, such as the annual regional GDP (
By the above algorithm of the adaptive Lasso, the estimated coefficients of the specific data for regional FDI in Central China are computed and outlined in Tab. 3.
It can be seen from the second line in Tab. 3 that
In order to verify the effectiveness and rationality of the adaptive Lasso grey model algorithm,RMSE (the root mean square error) [22] and MAE (the mean absolute error) are selected to evaluate it. Set
RMSE and MAE can be computed by this algorithm, and the results are shown in Tab. 4. It can be found that RMSE and MAE are relatively small, indicating that the selected variables can well reflect the factors related to the regional FDI statistics.
Based on the coefficients in Tab. 3, we select six primary factors affecting the mean value of FDI and eight main factors affecting the median value of FDI, and used the remaining part of the algorithm to predict the factors affecting regional FDI statistics from 2019 to 2023. The prediction accuracy is shown in Tabs. 5 and 6. The predicted and actual values of the affecting variables are obtained through Python and plotted in Figs. 1 and 2.
It can be seen from Figs. 1 and 2 that the predicted factor values of regional FDI statistics are close to the actual factor values, which indicates that what is predicted is valid. Moreover, Tabs. 5 and 6 demonstrate that these explanatory variables have many advantages, and various regional FDI statistics have different affecting factors. Considering the computed results and error analysis, the prediction accuracy of this algorithm is gererally satisfying, and the grey GM (1, 1) model combined with the adaptive Lasso model has a good effect on shortterm singlefactor prediction.
Using the adaptive Lasso grey model algorithm, the statistical data of regional FDI in six provinces of Central China from 2006 to 2023 were predicted . The comparison between the predictedand actual values of regional FDI is shown in Fig. 3.
Fig. 3 shows that the predicted values from 2006 to 2018 are very close to the actual value, and demonstrates that the adaptive Lasso grey model algorithm is valid in regional FDI statistics. It should be noted that no correlational FDI value could be forecasted with the fast change of the main factors of FDI statistics, the reasons of which is the focus of our future work.
By optimizing some traditional mathematical statistical methods, this paper proposes an adaptive Lasso grey model to predict regional FDI statistics. Based upon the characteristics of FDI data of six provinces of Central China, a test was designed to verify the effect of this adaptive Lasso grey model. Meanwhile, the feasibility and validity of the main algorithm of regional FDI statistics are demonstrated. This study also shows that the adaptive Lasso grey model with its algorithm and procedure can be extended to regional GDP and income study..
Acknowledgement: The author would like to thank the equipment support of Changsha University of Science and Technology as well as the support of the Fund Project.
Funding Statement: This work was supported in part by the National Key R&D Program of China (No. 2019YFE0122600), author H. H, https://service.most.gov.cn/; in part by the Project of Centre for Innovation Research in Social Governance of Changsha University of Science and Technology (No. 2017ZXB07), author J. H, https://www.csust.edu.cn/mksxy/yjjd/shzlcxyjzx.htm; in part by the Public Relations Project of Philosophy and Social Science Research Project of the Ministry of Education (No. 17JZD022), author J. L, http://www.moe.gov.cn/; in part by the Key Scientific Research Projects of Hunan Provincial Department of Education (No. 19A015), author J. L, http://jyt.hunan.gov.cn/; and in part by the Hunan 13th fiveyear Education Planning Project (No. XJK19CGD011), author J. H, http://ghkt.hntky.com/.
Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.
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