文献来源

1. Huang, W., et al. (2022). Convolutional neural network forecasting of European Union allowances futures using a novel unconstrained transformation method
1. Appendix A. Supplementary data【数据+R+Python】

基本理论

Vapnik（1998）提出的支持向量机(SVM)是基于统计学习理论的一种新的通用学习方法。SVM可以有效地解决人工神经网络的缺点，如网络构建问题、过拟合问题和局部最小困境（Kavousi-Fard等，2014）。目前，支持向量机已经成功地应用于许多领域。一般采用支持向量机进行分类问题。支持向量回归(SVR)旨在处理一般预测问题，包括用于回归的SVM版本（Beyca等，2019）。

1. Beyca, O. F., Ervural, B. C., Tatoglu, E., Ozuyar, P. G., & Zaim, S. (2019).Using machine learning tools for forecasting natural gas consumption in the province of Istanbul. Energy Economics.
2. Kavousi-Fard, A., Samet, H., & Marzbani, F. (2014).A new hybrid Modified Firefly Algorithm and Support Vector Regression model for accurate Short Term Load Forecasting. Expert Systems with Applications, 41(13), 6047–6056.
3. Vapnik,V.N. (1998). Statistical Learning Theory (Adaptive and Learning Systems for Signal Processing, Communications and Control). Wiley, New York.

示例代码

setwd("D:\\Download\\1-s2.0-S0140988322002171-mmc1\\Simulation Code and Data")
rm(list=ls())
library(e1071)
unconstrained_data<-read.csv("File_2_Data_After_Unconstrained_Transformation.csv", header=TRUE)
actual_data<-read.csv("File_1_Data_Before_Unconstrained_Transformation.csv", header=TRUE)
actual_Y<-actual_data[5:nrow(actual_data),]

# 构造输入数据集：EUA前4天的价格，前一天的解释变量
unconstrained_data_1<-unconstrained_data[4:(nrow(unconstrained_data)-1),2:5]
names(unconstrained_data_1)<-c("EUA_1_1","EUA_2_1","EUA_3_1","EUA_4_1")
unconstrained_data_2<-unconstrained_data[3:(nrow(unconstrained_data)-2),2:5]
names(unconstrained_data_2)<-c("EUA_1_2","EUA_2_2","EUA_3_2","EUA_4_2")
unconstrained_data_3<-unconstrained_data[2:(nrow(unconstrained_data)-3),2:5]
names(unconstrained_data_3)<-c("EUA_1_3","EUA_2_3","EUA_3_3","EUA_4_3")
unconstrained_data_4<-unconstrained_data[1:(nrow(unconstrained_data)-4),2:5]
names(unconstrained_data_4)<-c("EUA_1_4","EUA_2_4","EUA_3_4","EUA_4_4")
explantory_variables<-unconstrained_data[4:(nrow(unconstrained_data)-1),6:50]
explantory_variables[,45]<-as.factor(explantory_variables[,45])
# 自变量
explantory_data<-cbind(unconstrained_data_1,unconstrained_data_2,unconstrained_data_3,
unconstrained_data_4,explantory_variables)
# 因变量
response_variable<-unconstrained_data[5:nrow(unconstrained_data),2:5]

library(dummy)
explantory_data_dummy<-dummy(x=explantory_data)
for(i in 1:3){
explantory_data_dummy[,i]<-as.numeric(explantory_data_dummy[,i])
}
explantory_data<-cbind(explantory_data[,-61],explantory_data_dummy)

a<-explantory_data
b<-response_variable

response_variable_train<-b[1:(nrow(a)*0.8),]
explantory_data_train<-a[1:(nrow(b)*0.8),]

response_variable_test<-b[(nrow(a)*0.8+1):(nrow(a)+1),]
explantory_data_test<-a[(nrow(b)*0.8+1):(nrow(b)+1),]

actual_Y<-actual_Y[(nrow(actual_Y)*0.8+1):(nrow(actual_Y)+1),]

for(col in 1:4){
x<-explantory_data_train
y<-response_variable_train[,col]
model<-svm(x,y,type="nu-regression",kernel="linear",
gamma=if(is.vector(x)) 1 else 1/ ncol(x))
result<-predict(model,explantory_data_test)
if(col==1){
y1_pre<-result
}
if(col==2){
y2_pre<-result
}
if(col==3){
y3_pre<-result
}
if(col==4){
y4_pre<-result
}
}

flow<-exp(y1_pre)
fhigh<-exp(y1_pre)+exp(y2_pre)
flambda1<-exp(y3_pre)/(exp(y3_pre)+1)
flambda2<-exp(y4_pre)/(exp(y4_pre)+1)
fopen<-flambda1*fhigh+(1-flambda1)*flow
fclose<-flambda2*fhigh+(1-flambda2)*flow
fcenter<-(fhigh+flow)/2
frange<-(fhigh-flow)/2

open_MAPE<-0
high_MAPE<-0
low_MAPE<-0
close_MAPE<-0
open_MAE<-0
high_MAE<-0
low_MAE<-0
close_MAE<-0
open_RMSE<-0
high_RMSE<-0
low_RMSE<-0
close_RMSE<-0
RMSEH<-0
AR<-0
for(i in 1:length(fopen)){
#MAPE
open_MAPE<-open_MAPE+abs((fopen[i]-actual_Y[i,2])/actual_Y[i,2])
high_MAPE<-high_MAPE+abs((fhigh[i]-actual_Y[i,3])/actual_Y[i,3])
low_MAPE<-low_MAPE+abs((flow[i]-actual_Y[i,4])/actual_Y[i,4])
close_MAPE<-close_MAPE+abs((fclose[i]-actual_Y[i,5])/actual_Y[i,5])
#MAE
open_MAE<-open_MAE+abs((fopen[i]-actual_Y[i,2]))
high_MAE<-high_MAE+abs((fhigh[i]-actual_Y[i,3]))
low_MAE<-low_MAE+abs((flow[i]-actual_Y[i,4]))
close_MAE<-close_MAE+abs((fclose[i]-actual_Y[i,5]))
#RMSE
open_RMSE<-open_RMSE+abs((fopen[i]-actual_Y[i,2]))^2
high_RMSE<-high_RMSE+abs((fhigh[i]-actual_Y[i,3]))^2
low_RMSE<-low_RMSE+abs((flow[i]-actual_Y[i,4]))^2
close_RMSE<-close_RMSE+abs((fclose[i]-actual_Y[i,5]))^2
#RMSEH
center<-(actual_Y[i,3]+actual_Y[i,4])/2
range<-(actual_Y[i,3]-actual_Y[i,4])/2
RMSEH<-RMSEH+(abs(center-fcenter[i])+abs(range-frange[i]))^2
#AR
Y_u_fit<-fhigh[i]
Y_l_fit<-flow[i]
Y_upper_test<-actual_Y[i,3]
Y_lower_test<-actual_Y[i,4]
s=max(min(Y_u_fit,Y_upper_test)-max(Y_l_fit,Y_lower_test),0)
o=max(Y_u_fit,Y_upper_test)-min(Y_l_fit,Y_lower_test)-max(max(Y_l_fit,Y_lower_test)-min(Y_u_fit,Y_upper_test),0)
AR=AR+s/o
}
options(digits=5)
open_MAPE<-open_MAPE/length(fopen)
high_MAPE<-high_MAPE/length(fopen)
low_MAPE<-low_MAPE/length(fopen)
close_MAPE<-close_MAPE/length(fopen)
SVM_MAPE<-(open_MAPE+high_MAPE+low_MAPE+close_MAPE)/4

open_MAE<-open_MAE/length(fopen)
high_MAE<-high_MAE/length(fopen)
low_MAE<-low_MAE/length(fopen)
close_MAE<-close_MAE/length(fopen)
SVM_MAE<-(open_MAE+high_MAE+low_MAE+close_MAE)/4

open_RMSE<-(open_RMSE/length(fopen))^0.5
high_RMSE<-(high_RMSE/length(fopen))^0.5
low_RMSE<-(low_RMSE/length(fopen))^0.5
close_RMSE<-(close_RMSE/length(fopen))^0.5
SVM_RMSE<-((open_RMSE^2+high_RMSE^2+low_RMSE^2+close_RMSE^2)/4)^0.5
SVM_AR<-AR/length(fopen)

# 展示支持向量机的结果：MAPE MAE RMSE AR
SVM_MAPE
SVM_MAE
SVM_RMSE
SVM_AR

（完）