Abstract
This paper compares the most applicable models for the forecasting of time series. Models based on artificial neural networks nonlinear autoregressive neural network with external input (NARX), Elman’s neural network, and vector autoregression model were implemented. A special algorithm based on the analysis and prediction of the model residuals, which significantly improves the accuracy of the forecast, was proposed. For the prediction, we used the data of the main greenhouse gases methane (CH4) and water vapor (H2O) concentrations measured in summer 2016 in the surface layer of the atmospheric air on the Arctic island Belyy, Russia. The time interval of 192 h was chosen. The time interval was characterized by the significant daily variations in the CH4 concentration; the H2O concentrations did not have a pronounced trend. Values corresponding to the first 168 h of the interval were used for ANN training, and then, concentrations were predicted for the next 24 h. The accuracy of the prediction was determined by the set of errors and indices. The NARX model was more accurate than models based on Elman network and the VAR. The accuracy gain was from 16.5 to 40% for the models, which predicted the CH4 concentration, and from 21 to 58% for the models, which predicted the H2O concentration. The application of the proposed combined approach made it possible to increase the accuracy of the base model from 1.5 to 20% for the CH4 and from 4 to 20% for the H2O (depending on the corresponding errors and indices). The presented Taylor diagram was also showed the advantage of the proposed approach.








Similar content being viewed by others
Explore related subjects
Discover the latest articles and news from researchers in related subjects, suggested using machine learning.References
AMAP (2017) Snow, water, ice and permafrost. Summary for policy-makers. In: Arctic monitoring and assessment programme (AMAP), Oslo Norway, 20
Nullis C (2016) Provisional WMO statement on the status of the global climate in 2016. World Meteorological Organization
Serreze MC, Barry RG (2011) Processes and impacts of Arctic amplification: a research synthesis. Glob Planet Chang 77:85–96
Borrego C, Monteiro A, Pay MT, Ribeiro I, Miranda AI, Basart S, Baldasano JM (2011) How bias-correction can improve air quality forecasts over Portugal. Atmos Environ 37:6629–6641
Chu N, Kadane JB, Davidson CI (2010) Using statistical regressions to identify factors influencing PM2.5 concentrations: the Pittsburgh supersite as a case study. Aerosol Sci Technol 44:766–774
Cobourn WG (2010) An enhanced PM2.5 air quality forecast model based on nonlinear regression and back-trajectory concentrations. Atmos Environ 44:3015–3023
Sims CA (1980) Macroeconomics and reality. Econometrica 48(1):1–48
Olson DA, Riedel TP, Long R, Offenberg JH, Lewandowski M, Kleindienst TE (2019) Time series analysis of wintertime O3 and NOx formation using vector autoregressions. Atmos Environ. https://doi.org/10.1016/j.atmosenv.2019.116988
Zhang Y (2019) Dynamic effect analysis of meteorological conditions on air pollution: a case study from Beijing. Sci Total Environ 684:178–185
Wen L, Zhang X (2019) CO2 emissions in China’s Yangtze River economic zone: a dynamic vector autoregression approach. Pol J Environ Stud 28(2):923–933. https://doi.org/10.15244/pjoes/83668
Lin B, Xu B (2018) Growth of industrial CO2 emissions in Shanghai city: evidence from a dynamic vector autoregression analysis. Energy 151:167–177
Dmitriev AV (2013) Time series prediction of morbidity using artificial neural networks. Biomed Eng 47(1):43–45
Fernando HJS, Mammarella MC, Grandoni C, Fedele P, Di Marco R, Dimitrova R, Hyde P (2012) Forecasting PM10 in metropolitan areas: efficacy of neural networks. Environ Pollut 163:62–67
Genc DD, Yesilyurt C, Tuncel G (2010) Air pollution forecasting in Ankara, Turkey using air pollution index and its relation to assimilative capacity of the atmosphere. Environ Monit Assess 166:11–27
Russo A, Raischel F, Lind P (2013) Air quality prediction using optimal neural networks with stochastic variables. Atmos Environ 79:822–830
Zhang G (2003) Time series forecasting using a combined ARIMA and neural network model. Neurocomputing 50:159–175
Zhou Q, Jiang H, Wang J, Zhou J (2014) A combined model for PM2.5 forecasting based on ensemble empirical mode decomposition and a general regression neural network. Sci Total Environ 496:264–274
Wenquan X et al (2019) Deep belief network-based AR model for nonlinear time series forecasting. Appl Soft Comput 77:605–621
Chatfield C (2003) The analysis of time series: an introduction, vol 352, 6th edn. Chapman and Hall/CRC, London
Ardalani-Farsa M, Zolfaghari S (2010) Chaotic time series prediction with residual analysis method using combined Elman–NARX neural networks. Neurocomputing 73:2540–2553
Erdil A, Arcaklioglu E (2013) The prediction of meteorological variables using artificial neural network. Neural Comput Appl 22:1677–1683
Menezes JM Jr, Barreto GA (2008) Long-term time series prediction with the NARX network: an empirical evaluation. Neurocomputing 71:3335–3343
Pisoni E, Farina M, Carnevale C, Piroddi L (2009) Forecasting peak air pollution levels using NARX models. Eng Appl Artif Intell 22:593–602
Zemouri R, Gouriveau R, Zerhouni N (2010) Defining and applying prediction performance metrics on a recurrent NARX time series model. Neurocomputing 73:2506–2521
Sergeev A, Shichkin A, Buevich A (2018) Time series forecasting of methane concentrations in the surface layer of atmospheric air in Arctic region. In: Proceedings of the 44th international conference on applications of mathematics in engineering and economics AMEE 2018, American Institute of Physics Inc., vol 2048, p 060005. https://doi.org/10.1063/1.5082120
Ren Guanghua, Cao Yuting, ShipingWen Tingwen Huang, Zeng Zhigang (2018) A modified Elman neural network with a new learning rate scheme. Neurocomputing 286:11–18. https://doi.org/10.1016/j.neucom.2018.01.046
Dai F, Zhoua O, Lva Z, Wang X, Liu G (2014) Spatial prediction of soil organic matter concentration integrating artificial neural network and ordinary kriging in Tibetan Plateau. Ecol Ind 45:184–194
Sergeev AP, Buevich AG, Baglaeva EM, Shichkin AV (2019) Combining spatial autocorrelation with machine learning increases prediction accuracy of soil heavy metals. CATENA 174:425–435
Tarasov DA, Buevich AG, Sergeev AP, Shichkin AV (2018) High variation topsoil pollution forecasting in the Russian Subarctic: using artificial neural networks combined with residual kriging. Appl Geochem 88(B):188–197
Shepherd AJ (1997) Second-order methods for neural networks: fast and reliable training methods for multi-layer perceptrons, vol 145. Springer, Berlin
Taylor KE (2001) Summarizing multiple aspects of model performance in a single diagram. J Geophys Res 106(D7):7183–7192
Willmott CJ (1981) On the validation of models. Phys Geogr 2:184–194
Willmott CJ, Robeson SM, Matsuura K (2011) A refined index of model performance. Int J Climatol. https://doi.org/10.1002/joc.2419Wiley Online Library (wileyonlinelibrary.com)
Sabolova R, Seckarova V, Dusek J, Stehlik M (2015) Entropy based statistical inference for methane emissions released from wetland. Chemometr Intell Lab Syst 141:125–133
Jordanova P, Dusek J, Stehlik M (2013) Microergodicity effects on ebullition of methane modelled by Mixed Poisson process with Pareto mixing variable. Chemometr Intell Lab Syst 128:124–134
Acknowledgements
Authors want to thank the editor and anonymous reviewers for their constructive comments that contributed to improving the paper.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
Authors declare that there is no conflict of interests regarding the publication of this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Buevich, A., Sergeev, A., Shichkin, A. et al. A two-step combined algorithm based on NARX neural network and the subsequent prediction of the residues improves prediction accuracy of the greenhouse gases concentrations. Neural Comput & Applic 33, 1547–1557 (2021). https://doi.org/10.1007/s00521-020-04995-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-020-04995-4