The forecasting assessment There are three metrics used in this paper to assess the forecast performance of the model, namely MAPE, MAE, and MSE, which are defined as follows: MAPE=1ni=1nyi-yiyi×100% (16) MAE=1ni=1nyi-yi (17) MSE=1ni=1nyi-yi2 (18) For the indexes of MAPE, MAE, and MSE, the lower the index value, the higher the forecasting accuracy. The improvement rate of the corresponding model is calculated to determine whether the forecast accuracy of the model is higher than the compared model. The index improvement rates are defined as follows:

这段话也没有发现任何语法错误。该段介绍了本文中用于评估模型预测性能的三个指标，分别是MAPE、MAE和MSE，它们的定义如下：MAPE=1/n × Σi=1n |(yi-^yi)/yi| × 100%（16），MAE=1/n × Σi=1n |yi-^yi|（17），MSE=1/n × Σi=1n (yi-^yi)2（18）。对于MAPE、MAE和MSE指标，指标值越低，预测精度越高。通过计算相应模型的指标改进率，确定该模型的预测精度是否高于比较模型。指标改进率的定义如下：

相关问题

Step 4. GM-GRA-DPC-PSOSVR combined forecasting. The forecasting results of individual models are as the inputs to PSOSVR for establishing nonlinear combination, and the whole procedure based on Step 1 to Step 4 is called GM-GRA-DPC-PSOSVR model. Step 5. Forecasting comparisons. In order to test the effectiveness of the forecasting models, this research introduces MAPE(Mean Absolute Percentage Error), MAE(Mean Absolute Error), MSE, and improvement rates to compares the forecasting ability of GM-GRA-DPC-PSOSVR with individual forecasting models.

这段话也没有发现任何语法错误。该段介绍了GM-GRA-DPC-PSOSVR模型的构建过程中的第四步和第五步，即使用PSOSVR建立个体模型的非线性组合，整个过程基于步骤1到步骤4被称为GM-GRA-DPC-PSOSVR模型。为了测试预测模型的有效性，该研究引入MAPE（平均绝对百分比误差）、MAE（平均绝对误差）、MSE和改进率来比较GM-GRA-DPC-PSOSVR与个体预测模型的预测能力。

Step 2. Establishing candidate models for carbon emission forecasting. GM(1,1) is employed to forecast the carbon emission for the three provinces, the residual is the difference between actual data and the forecasting of GM(1,1). The residuals are respectively predicted by SVR, GWOSVR, PSOSVR and PSOGSASVR, where inputs are the different lags of influencing factors. Taking Qinghai as an example, the number of influencing factors is 3 and lag order is 3, so there are 3^3\ast4=108 individual models.

这段话也没有发现任何语法错误。该段介绍了GM-GRA-DPC-PSOSVR模型的构建过程中的第二步，即建立碳排放预测的候选模型。使用GM(1,1)对三个省份的碳排放进行预测，残差是实际数据与GM(1,1)预测值之间的差异。残差分别由SVR、GWOSVR、PSOSVR和PSOGSASVR进行预测，其中输入是影响因素的不同滞后期。以青海省为例，影响因素的数量为3，滞后期为3，因此有108个个体模型。