﻿ 基于Lasso方法的我国能源消费影响因素分析 Analysis of Energy Consumption Influencing Factors in China Based on the Lasso Method

Statistics and Application
Vol.06 No.01(2017), Article ID:19904,8 pages
10.12677/SA.2017.61007

Analysis of Energy Consumption Influencing Factors in China Based on the Lasso Method

Xiaotong Li, Danyan Qin, Minghui Lv

Science College, China University of Petroleum, Beijing

Received: Feb. 25th, 2017; accepted: Mar. 14th, 2017; published: Mar. 17th, 2017

ABSTRACT

With the acceleration of economic development and the increasing demand for resources, energy consumption shows a rising trend in recent years. To ensure the stable, sustainable and healthy development of China’s economy, it is necessary to study on consumption factors and to forecast energy consumption demand reasonably. As so far, scholars have used simple linear regression, principal component regression and ridge regression method for analyzing China’s energy consumption factors, but models achieved from these studies may be too lean to find more comprehensive energy consumption factors. While according to the related data of domestic energy consumption during 2000-2012, this paper chooses a new method—Lasso method to make regression model for domestic energy consumption, and then we get the main energy consumption effecting factors: economic development, demographic factor, industrial structure, technological progress, energy consumption efficiency and energy price factor, so we can control energy consumption through these main factors. Additionally, we use stepwise regression and ridge regression to make regression models, the results got from the Lasso, stepwise regression and ridge regression are compared, the study shows the Lasso method is better than the other methods in terms of variable selection, because it could find more comprehensive energy consumption factors; for predictions of 2013 and 2014, Lasso method is more accurate than the other two methods.

Keywords:Energy Consumption, Lasso, Stepwise Regression, Ridge Regression

1. 引言

Lasso回归提出至今，已被广泛应用在生物医学、金融分析、图像处理、机器学习等众多领域，它在变量选择与参数压缩估计方面表现比较好。Lasso回归根据与被解释变量相关性的大小来选择回归方程中的解释变量，能使最终模型既简洁又不丢失与被解释变量密切相关的解释变量，且有较高的预测精度。本文用Lasso方法对我国能源消费的影响因素进行分析，首先我们根据问题的实际背景以及获取数据的局限性初步给出了七个影响我国能源消费的因素，分别为：经济增长因素、人口增长因素、产业结构因素、技术进步因素、投资因素、能源利用效率因素以及能源价格因素。基于2000年~2012年我国能源消费总量的相关数据，我们选用了Lasso方法对我国能源消费影响因素建立了回归模型，得到了影响我国能源消费的主要因素以及给出了2013、2014年能源消费总量的预测值。同时我们还利用逐步回归和岭回归对能源消费影响因素这一问题分别建立回归模型，并将Lasso方法得到的结果与其在变量选择、预测精度方面进行了比较，在变量选择即能源消费影响因素的选择方面，Lasso方法比其他两种方法更为全面地找出能源消费的主要影响因素，在能源消费总量的预测方面，Lasso方法比其他两种方法更为精确。

2. Lasso方法的介绍

Robert Tibshirani于1996提出了一种新的变量选择技术Lasso [7] ，即Least Absolute Shrinkage and Selection Operator。此方法用模型系数的绝对值函数作为惩罚来压缩模型系数，使一些回归系数缩小，甚至使一些绝对值较小的系数直接变为0。

(1)

(2)

(3)

Lasso问题的求解实质是解一个带不等式约束的二次规划问题，Bradley Efron (2004) [8] 等提出的最小角回归(Least Angle Regression)算法，和著名的向前选择法(Forward Selection)一样，一开始令所有的系数为零，先找出和因变量相关性最强的自变量，记为，然后我们沿着的方向上找出另一个自变量，记为，使得它与当前的残差有同样的相关性。接下来不同于向前选择法继续沿着的方向，最小角回归算法沿着平分前两个变量夹角的方向，找到变量，使得它满足相关性最强，然后在沿着平分前三个变量夹角的方向找第四个变量，以此类推，直到找到所有变量，算法终止。对最小角回归算法的一个修正即要求进行每一步计算时要求当前得到的估计值必须与相关系数符号一致，这就能得到了Lasso算法，从而也就解决Lasso方法的计算问题。

3. 我国能源消费影响因素的实证分析

3.1. 我国能源消费影响因素指标的选取以及数据来源

3.2. 基于Lasso方法的模型的建立

Table 1. Index selection

Table 2. 2000~2012 Annual data

Table 3. The value of the Lasso variable selection path and the value of various criteria statistics

Figure 1. Multicollinearity diagnosis

Figure 2. Lasso Regression path graph

3.3. 三种回归分析结果的比较

Table 4. Standardized parameter estimation

4. 结论

Table 5. Comparison of the results of Lasso regression, ridge regression and stepwise regression

Analysis of Energy Consumption Influencing Factors in China Based on the Lasso Method[J]. 统计学与应用, 2017, 06(01): 73-80. http://dx.doi.org/10.12677/SA.2017.61007

1. 1. 佟阿思根, 侯俊芝. 中国能源消费现状及能源需求预测[J]. 内蒙古民族大学学报, 2008(3): 83-85.

2. 2. 赵建辉. 基于主成分回归模型的我国能源消费影响因素分析[J]. 中国矿业, 2014(1): 44-49.

3. 3. 张丹平. 基于岭回归方法的我国能源消费影响因素研究[J]. 统计与决策, 2012(21): 146-148.

4. 4. Geem, Z.W. and Roper, W.E. (2009) Energy Demand Estimation of South Korea Using Artificial Neural Network. Energy Policy, 37, 4049-4054. https://doi.org/10.1016/j.enpol.2009.04.049

5. 5. Ekonomou, L. (2010) Greek Long-Term Energy Consumption Prediction Using Artificial Neural Networks. Energy, 35, 512-517. https://doi.org/10.1016/j.energy.2009.10.018

6. 6. Oludolapo, O.A., Jimoh, A.A. and Kholopane, P.A. (2012) Comparing Performance of MLP and RBF Neural Network Models for Predicting South Africa’s Energy Consumption. Journal of Energy in Southern Africa, 23, 40-46.

7. 7. Tibshirani, R. (1996) Regression Shrinkage and Selection via the Lasso. Journal of the Royal Statistical Society. Series B (Methodological), 58, 267-288.

8. 8. Efron, B., Hastie, T., Johnstone, I., et al. (2004) Least Angle Regression. The Annals of Statistics, 32, 407-499. https://doi.org/10.1214/009053604000000067

9. 9. 高惠璇, 耿直, 李贵斌, 等. SAS系统SAS/STAT软件使用手册[M]. 北京: 中国统计出版社, 1997.