指数平滑与自回归融合预测模型及实证

doi:10.3778/j.issn.1002-8331.2010-0247

摘要/Abstract

摘要： 针对银行业务中的隔夜头寸预测问题，融合指数平滑与自回归预测的思想方法，提出了一个时间序列一步预测的微分动力学方程，证明了方程的离散化结构同无隐层BP神经网络的等价性。讨论了模型预测有效性问题，并进行了实证分析。对12个样本预报偏差的拟合优度检验表明，绝对预报偏差近似服从指数分布；实证分析了环比波动特征同模型预报误差以及预报同态度的关系，表明在一定条件下模型的预报是有效的，同NLP框架下的LSTM和GRU进行了对比实验表明该模型有更好的表现；定义了稳态指数和转折指数来描述时间序列的环比波动特征，分析表明稳态指数和转折指数可以预估模型预报的误差水平和同态度水平；研究了模型前端降噪对预报结果的影响，结果表明前端降噪可以抑制模型预报的“过敏”行为，有利于对时间序列变化趋势的动态跟踪。

关键词: 时间序列预测, 指数平滑, 自回归, BP神经网络, 实证分析

Abstract: To solve the problem of overnight position prediction in banking business, a differential dynamic equation for one-step prediction of time series is proposed by integrating exponential smoothing and autoregressive prediction. It is proved that the discretization structure of the equation is equivalent to that of BP neural network without hidden layer. Then, the prediction validity of the model is discussed and an empirical analysis is made. Firstly, the goodness of fit test of 12 samples shows that the absolute prediction deviation approximately follows the exponential distribution. Secondly, the empirical analysis of the relationship between the ring ratio fluctuation characteristics and the prediction error, as well as the relationship between ring ratio fluctuation characteristics and the prediction homomorphism rate, shows that the prediction of the model is effective under certain conditions. In addition, the model is compared with LSTM and GRU in NLP framework. It is found that the model in this paper has better performance. Thirdly, the steady-state index and turning index are defined to describe the month on month fluctuation characteristics of time series. The results reflect that the steady-state index and turning index can predict the error level and homomorphism level of the model prediction. Finally, the influence of the front-end noise reduction on the prediction results is discussed. The results are indicative that the front-end noise reduction can suppress the “allergic” behavior of the model prediction, which is conducive to the dynamic tracking of the change trend of the time series.

Key words: time series prediction, exponential smoothing, autoregression, BP neural network, empirical analysis

包研科, 陈然, 郑宏杰, 冯永安, 王江. 指数平滑与自回归融合预测模型及实证[J]. 计算机工程与应用, 2022, 58(14): 269-281.

BAO Yanke, CHEN Ran, ZHENG Hongjie, FENG Yong’an, WANG Jiang. Index Smoothing and Autoregressive Fusion Forecasting Model and Its Empirical Study[J]. Computer Engineering and Applications, 2022, 58(14): 269-281.

参考文献

[1] 张美英，何杰.时间序列预测模型研究综述[J].数学的实践与认识，2011，41（18）：189-195.
ZHANG M Y，HE J.Summary on time series forecasting model[J].Mathematics in Practice and Theory，2011，41（18）：189-195.
[2] 中国人民银行调查统计司.时间序列X-12-ARIMA季节调整─原理与方法[M].北京：中国金融出版社，2006.
Investigation and Statistics Department of the People’s Bank of China.Seasonal adjustment of time series X-12-ARIMA：principle and method[M].Beijing：China Finance Press，2006.
[3] 高铁梅.计量经济分析方法与建模─Eviews应用及实例[M].北京：清华大学出版社，2006.
GAO T M.Econometric analysis method and modeling-Eviews application and example[M].Beijing：Tsinghua University Press，2016.
[4] BOX G P E，JENKINS G M.Time series analysis：forecasting and control[J].The Statistician，1978，27：265.
[5] 何书元.应用时间序列分析[M].北京：北京大学出版社，2004.
HE S Y.Application of time series analysis[M].Beijing：Peking University Press，2004.
[6] CHEN Z.Research on forecasting method of balance treasure fund flow[C]//2017 16th International Symposium on Distributed Computing and Applications to Business，Engineering and Science（DCABES），2017.
[7] KHANARSA P，SINAPIROMSARAN K.Multiple ARIMA subsequences aggregate time series model to forecast cash in ATM[C]//2017 9th International Conference on Knowledge and Smart Technology（KST），2017.
[8] 范维，张磊，石刚.季节调整方法综述及比较[J].统计研究，2006（2）：70-73.
FAN W，ZHANG L，SHI G.The comprehensive description and comparison of seasonal adjusting methods[J].Statistical Research，2006（2）：70-73.
[9] 潘和平，张承钊.FEPA-金融时间序列自适应组合预测模型[J].中国管理科学，2018，26（6）：26-38.
PAN H P，ZHANG C Z.FEPA：an adaptive integrated prediction model of financial time series[J].Chinese Journal of Management Science，2018，26（6）：26-38.
[10] WILLIAMS R J，ZIPSER D.A lesrning algorithm for continually running fully recurrent neuralnetworks[J].Neural Computation，1989，1（2）：270-280.
[11] HOCHREITER S，SCHMIDHUBER J.Long short-term memory[J].Neural Computation，1997，9（8）：1735-1780.
[12] CHO K，VAN M B，GULCEHER C，et al.Learning phrase representations using RNN encoder-decoder for statistical machine translation[J].arXiv：1406.1078，2014.
[13] MAASS W.Networks of spiking neurons：the third generation of neural network models[J].Neural Networks，1997，10（9）：1659-1671.
[14] 廖大强，印鉴.基于多分支RNN快速学习算法的混沌时间序列预测[J].计算机应用研究，2015，32（2）：403-408.
LIAO D Q，YIN J.Chaotic time series of fast learning algorithm of multi branch prediction based on RNN[J].Research on Computer Application，2015，32（2）：403-408.
[15] 古勇，苏宏业，褚健.循环神经网络建模在非线性预测控制中的应用[J].控制与决策，2000（2）：254-256.
GU Y，SU H Y，CHU J.Recurrent neural network modeling and its application in nonlinear predictive control[J].Control and Decision，2000（2）：254-256.
[16] MA X L，YU H Y，WANG Y P，et al.Large-scale transportation network congestion evolution prediction using deep learning theory[J].Plos One，2015，10（3）：e0119044.
[17] ZHANG L，FAN X，XU C.A fusion financial prediction strategy based on RNN and representative pattern discovery[C]//the 18th International Conference on Parallel and Distributed Computing，Applications and Technologies（PDCAT’17），2017.
[18] 王鑫，吴际，刘超，等.基于LSTM循环神经网络的故障时间序列预测[J].北京航空航天大学学报，2018，44（4）：772-784.
WANG X，WU J，LIU C，et al.Exploring LSTM based recurrent neural network for fault time series prediction[J].Journal of Beijing University of Aeronautics and Astronautics，2018，44（4）：772-784.
[19] 黄婷婷，余磊.SDAE-LSTM模型在金融时间序列预测中的应用[J].计算机工程与应用，2019，55（1）：142-148.
HUANG T T，YU L.Application of SDAE-LSTM model on financial time series forecasting[J].Computer Engineering and Applications，2019，55（1）：142-148.
[20] 罗向龙，李丹阳，杨彧，等.基于KNN-LSTM的短时交通流预测[J].北京工业大学学报，2018，44（12）：1521-1527.
LUO X L，LI D Y，YANG Y，et al.Short-term traffic flow prediction based on KNN-LSTM[J].Journal of Beijing University of Technology，2018，44（12）：1521-1527.
[21] LIU Y，DONG S，LU M，et al.LSTM based reserve prediction for bank outlets[J].Tsinghua Science and Technology，2019，24（1）：77-85.
[22] CHUNG J，GULCEHRE C，CHO K H，et al.Empirical evaluation of gated recurrent neural networks on sequence modeling[C]//NIPS 2014 Deep Learning and Representation Learning Workshop，2014：1-9.
[23] HUYNH H D，DANG L M，DUONG D.A new model for stock price movements prediction using deep neural network[C]//Proceedings of the Eighth International Symposium on Information and Communication Technology.New York，NY：ACM Press，2017：57-62.
[24] 张金磊，罗玉玲，付强.基于门控循环单元神经网络的金融时间序列预测[J].广西师范大学学报（自然科学版），2019，37（2）：82-89.
ZHANG J L，LUO Y L，FU Q.Predicting financial time series based on gated recurrent unit neural network[J].Journal of Guangxi Normal University（Natural Science Edition），2019，37（2）：82-89.
[25] XIUYUN G，YING W，YANG G，et al.Short-term load forecasting model of GRU network based on deep learning framework[C]//2018 2nd IEEE Conference on Energy Internet and Energy System Integration（EI2），2018.
[26] HOSSAIN M A，KARIM R，THULASIRAM R，et al.Hybrid deep learning model for stock price prediction[C]//2018 IEEE Symposium Series on Computational Intelligence（SSCI），2018.
[27] JIA P，LIU H，WANG S，et al.Research on a mine gas concentration forecasting model based on a GRU network[J].IEEE Access，2020，8：38023-38031.
[28] MAASS W.Noisy spiking neurons with temporal coding have more computational power than sigmoidal neurons[EB/OL].[2019-12-10].http：//papers.nips.cc/paper/1307-noisy-spiking-neuronswith-temporal-coding-have-more-computational-power-than-sigmoidalneurons.pdf.
[29] 陈通，孙国强，卫志农，等.基于Spiking神经网络的光伏系统发电功率预测[J].电力系统及其自动化学报，2017，29（6）：7-12.
CHEN T，SUN G Q，WEI Z N，et al.Power generation forecasting for photovoltaic system based on spiking neural network[J].Proceedings of the CSU-EPSA，2017，29（6）：7-12.
[30] LAPEDES A，FARBER R.Nonlinear signal processing using neural networks：prediction and system modelling[C]//IEEE International Conference on Neural Networks，1987.
[31] 沈良峰，张月龙.基于指数平滑技术的边坡位移预测方法[J].建筑科学，2004（4）：43-45.
SHEN L F，ZHANG Y L.Forecasting method of the slope displacement based on the exponential smoothing technology[J].Building Science，2004（4）：43-45.
[32] 徐健学，蒋耀林，江俊，等.非线性科学的研究主流综述[J].飞行力学，1996（1）：17-22.
XU J X，JIANG Y L，JIANG J，et al.Review of mainstream research on nonlinear science[J].Flight Dynamics，1996（1）：17-22.
[33] GEMULLA R，NIJKAMP E，HAAS P J，et al.Large-scale matrix factorization with distributed stochastic gradient descent[C]//NIPS Big Learn Workshop，2011：69-77.
[34] SIAMI-NAMINI S，NAMIN A S.Forecasting economics and financial time series：ARIMA vs.LSTM[J].arXiv：1803.
06386，2018.