基于混合分位数与时变权重组合的碳价格区间预测研究

doi:10.16381/j.cnki.issn1003-207x.2024.1451

摘要/Abstract

摘要：

鉴于现有碳价区间预测模型在追求高覆盖率时常面临区间过宽的问题，本文创新性地提出了一种基于混合分位数的时变权重组合预测模型。首先对Transformer架构进行了优化，通过时序分块与两阶段平稳处理策略，大幅减少了模型参数量，避免了数据分布特性被过度平滑所损耗，从而增强了模型的稳定性和预测准确性。接着，结合TimesNet模型的多周期特征识别能力，分别进行混合分位数预测。针对时间序列数据随时间变化的特点，本文开发了一种基于多目标优化的上下界时变权重组合算法，有效地融合了两种预测模型的优点，实现了区间宽度与覆盖率之间的合理平衡。实验结果显示，本文提出的模型在多个碳交易试点应用中表现优异，显著提高了预测区间的适用性和精确度，为行业从业者提供了一种既能保证覆盖率又能控制区间宽度的碳价预测新方法。

关键词: 时间序列预测, 不确定性分析, 深度学习

Abstract:

The accurate prediction of carbon prices provides valuable information to practitioners， supports market development， and help the dual-carbon target to be realized on schedule. Therefore， how to construct an efficient， accurate and stable carbon price prediction model has become a major research issue. However， carbon price interval prediction poses significant challenges due to the need to balance interval width and coverage. An innovative time-varying weighted ensemble interval prediction model， based on mixed quantile regression， is proposed to quantify the uncertainty of carbon prices. Two hybrid quantile models are constructed using advanced time-series deep learning algorithms for predicting carbon price intervals. To improve prediction precision， a multi-objective optimization algorithm is developed， dynamically assigning time-varying weights to optimize the upper and lower bounds of combined interval predictions， striking a balance between interval width and coverage. Historical carbon trading data from two representative Chinese pilots， sourced from the Wind database， are used for empirical validation. The results demonstrate that the proposed model performs robustly across various pilot applications， significantly enhancing the reliability and precision of prediction intervals. A valuable tool is provided for practitioners， enabling carbon price predictions with high coverage while effectively controlling interval width.

Key words: time series forecasting, uncertainty analysis, deep learning

中图分类号:

TK89

王聚杰,张欣. 基于混合分位数与时变权重组合的碳价格区间预测研究[J]. 中国管理科学, 2026, 34(4): 298-308.

Jujie Wang,Xin Zhang. Carbon Price Interval Forecasting Study Based on the Hybrid Quantile and Time-Varying Weights[J]. Chinese Journal of Management Science, 2026, 34(4): 298-308.

图/表 12

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图2

表1

碳价区间预测评估指标"

评估指标	定义	公式
PIAW	区间平均宽度	$P I A W = ∑ n = 1 N U n - L n N$
PINAW	区间归一化平均宽度	$P I N A W = ∑ n = 1 N U n - L n N * R$ ， $R = m a x (P n) - m i n (P n)$
PICP	区间覆盖率	$P I C P = ∑ n = 1 N c n N, c n = 1, P n ∈ [L n, U n] 0, P n ∉ [L n, U n]$
MPICD	平均区间中心偏差	$M P I C D = 1 / N ∑ n = 1 N U n + L n 2 - P n$
AWD	累积宽度偏差	$A W D = ∑ n = 1 N A W D n$ ， $A W D n = L n - P n U n - L n, P n < L n 0, P n ∈ L n, U n P n - U n U n - L n, P n > L n$

表1

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图5

表2

图6

表3

图7

图8

表4

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试点	样本量	均值	标准差	最小值	25%	50%	75%	最大值	偏度	峰度
广东	2084	35.62	24.37	8.10	15.29	27.06	60.24	95.26	0.85	-0.83
湖北	2149	28.42	10.89	10.38	20.90	26.29	33.35	61.48	0.60	-0.63

试点	预测模型	评估指标	90%置信区间	95%置信区间	99%置信区间
广东	TimesNet	PIAW	4.9707	6.4727	12.0167
		PINAW	0.1884	0.2453	0.4554
		PICP	87.8553	93.5401	99.2248
		MPICD	1.2588	1.2891	1.0609
		AWD	10.6520	4.7815	0.5437
	NPatch-Transformer	PIAW	1.9174	2.5889	4.9693
		PINAW	0.0727	0.0981	0.1883
		PICP	58.9147	67.9587	88.1137
		MPICD	0.9845	0.9902	1.0609
		AWD	104.0048	58.7865	10.1403
湖北	TimesNet	PIAW	6.9430	9.2918	13.4438
		PINAW	0.2394	0.3204	0.4636
		PICP	92.0000	95.7500	98.7500
		MPICD	1.2158	1.2778	1.4227
		AWD	9.8612	4.5588	1.8592
	NPatch-Transformer	PIAW	2.0910	3.0382	6.2523
		PINAW	0.0721	0.1048	0.2156
		PICP	75.0000	87.2500	97.0000
		MPICD	0.7405	0.7385	1.1602
		AWD	48.7236	23.1186	3.7926

试点	组合算法	评估指标	90%置信区间	95%置信区间	99%置信区间
广东	单目标优化	PIAW	2.1950	2.9419	5.6100
		PINAW	0.0832	0.1115	0.2126
		PICP	63.5659	71.8346	93.7984
		MPICD	0.9956	1.0042	1.0334
		AWD	74.4730	40.2967	5.4947
	多目标时变优化	PIAW	3.4808	4.6129	8.5559
		PINAW	0.1319	0.1748	0.3242
		PICP	78.5530	88.1137	97.1576
		MPICD	1.1033	1.1330	1.0909
		AWD	25.5929	12.9593	1.9371
湖北	单目标优化	PIAW	2.5321	3.6067	6.9060
		PINAW	0.0873	0.1244	0.2381
		PICP	82.5000	91.0000	97.7500
		MPICD	0.7447	0.7380	1.0571
		AWD	30.4614	14.1638	2.6147
	多目标时变优化	PIAW	4.5970	6.1485	9.8145
		PINAW	0.1585	0.2120	0.3384
		PICP	91.7500	96.5000	98.7500
		MPICD	0.9441	0.9709	1.0262
		AWD	13.2713	5.9440	1.6238