Nonlinear combination method of forecasters applied to PM time series

Abstract Hybrid systems that combine Artificial Neural Networks with other forecasters have been widely employed for time series forecasting. In this context, some architectures use temporal patterns extracted from the error series (residuals), i.e., the difference between the time series and the forecasting of this time series. These architectures have reached relevant theoretical and practical results. However, in the learning process of complex time series using these hybrid systems two open questions arise: it is hard to ensure that the linear and nonlinear patterns, underlying the time series, are properly modeled; and the best function to combine the time series forecaster and error series forecaster is unknown. In this context, this work proposes a Nonlinear Combination (NoLiC) method to combine forecasters. The NoLiC method is a hybrid system that is composed of two steps: i) estimation of the models’ parameters for the time series and their respective residuals, and ii) search for the best function that combines these models using a multi-layer perceptron. Experimental simulations are conducted using four real-world complex time series of great importance for public health and evaluated using six performance measures. The results show that the NoLiC method reaches superior results when compared with literature works.

[1]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[2]  André Nel,et al.  ATMOSPHERE: Enhanced: Air Pollution-Related Illness: Effects of Particles , 2005 .

[3]  F. Dominici,et al.  Particulate Matter Matters , 2014, Science.

[4]  Paulo S. G. de Mattos Neto,et al.  Error modeling approach to improve time series forecasters , 2015, Neurocomputing.

[5]  George D. C. Cavalcanti,et al.  An Approach to Improve the Performance of PM Forecasters , 2015, PloS one.

[6]  Hisham Ettouney,et al.  Forecasting of ozone pollution using artificial neural networks , 2009 .

[7]  Ying Wang,et al.  A Hybrid Model for Predicting the Prevalence of Schistosomiasis in Humans of Qianjiang City, China , 2014, PloS one.

[8]  Michael Jerrett,et al.  Atmospheric science: The death toll from air-pollution sources , 2015, Nature.

[9]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[10]  Yi-Ming Wei,et al.  Carbon price forecasting with a novel hybrid ARIMA and least squares support vector machines methodology , 2013 .

[11]  R. Clemen.  Combining forecasts: A review and annotated bibliography , 1989 .

[12]  Amy Loutfi,et al.  A review of unsupervised feature learning and deep learning for time-series modeling , 2014, Pattern Recognit. Lett..

[13]  R. K. Agrawal,et al.  A combination of artificial neural network and random walk models for financial time series forecasting , 2013, Neural Computing and Applications.

[14]  George D. C. Cavalcanti,et al.  Hybrid intelligent system for air quality forecasting using phase adjustment , 2014, Eng. Appl. Artif. Intell..

[15]  Mehdi Khashei,et al.  A novel hybridization of artificial neural networks and ARIMA models for time series forecasting , 2011, Appl. Soft Comput..

[16]  Gavin C. Cawley,et al.  Extensive evaluation of neural network models for the prediction of NO2 and PM10 concentrations, compared with a deterministic modelling system and measurements in central Helsinki , 2003 .

[17]  Guoqiang Peter Zhang,et al.  Time series forecasting using a hybrid ARIMA and neural network model , 2003, Neurocomputing.

[18]  Paulo S. G. de Mattos Neto,et al.  Correcting and combining time series forecasters , 2014, Neural Networks.

[19]  Alan Bensoussan,et al.  Traditional Chinese Medicine in Cancer Care: A Review of Controlled Clinical Studies Published in Chinese , 2013, PloS one.

[20]  Bijari Mehdi,et al.  WHICH METHODOLOGY IS BETTER FOR COMBINING LINEAR AND NONLINEAR MODELS FOR TIME SERIES FORECASTING , 2011 .

[21]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[22]  Ying Wang,et al.  Application of a New Hybrid Model with Seasonal Auto-Regressive Integrated Moving Average (ARIMA) and Nonlinear Auto-Regressive Neural Network (NARNN) in Forecasting Incidence Cases of HFMD in Shenzhen, China , 2014, PloS one.

[23]  J. M. Bates,et al.  The Combination of Forecasts , 1969 .

[24]  Mehdi Khashei,et al.  Combining seasonal ARIMA models with computational intelligence techniques for time series forecasting , 2012, Soft Comput..

[25]  X. Miao,et al.  Application of a Hybrid Model for Predicting the Incidence of Tuberculosis in Hubei, China , 2013, PloS one.

[26]  Jun Miao,et al.  Robust regression with extreme support vectors , 2014, Pattern Recognit. Lett..

[27]  Ali S. Hadi,et al.  ARCH and GARCH Models , 2010 .

[28]  Xuguo Zhou,et al.  Validation of Reference Housekeeping Genes for Gene Expression Studies in Western Corn Rootworm (Diabrotica virgifera virgifera) , 2014, PloS one.

[29]  Mikko Kolehmainen,et al.  Evaluation of an integrated modelling system containing a multi-layer perceptron model and the numerical weather prediction model HIRLAM for the forecasting of urban airborne pollutant concentrations , 2005 .

[30]  J. Kukkonen,et al.  Intercomparison of air quality data using principal component analysis, and forecasting of PM₁₀ and PM₂.₅ concentrations using artificial neural networks, in Thessaloniki and Helsinki. , 2011, The Science of the total environment.

[31]  Paulo S. G. de Mattos Neto,et al.  Measurement of Fitness Function efficiency using Data Envelopment Analysis , 2014, Expert Syst. Appl..

[32]  Ari Karppinen,et al.  Evaluation of a multiple regression model for the forecasting of the concentrations of NOx and PM10 in Athens and Helsinki. , 2011, The Science of the total environment.

[33]  Francesca Dominici,et al.  Coarse particulate matter air pollution and hospital admissions for cardiovascular and respiratory diseases among Medicare patients. , 2008, JAMA.

[34]  Maurizio Filippone,et al.  A comparative evaluation of nonlinear dynamics methods for time series prediction , 2009, Neural Computing and Applications.

[35]  Durdu Ömer Faruk.  A hybrid neural network and ARIMA model for water quality time series prediction , 2010, Eng. Appl. Artif. Intell..

[36]  Michael Y. Hu,et al.  Forecasting with artificial neural networks: The state of the art , 1997 .

[37]  Çagdas Hakan Aladag,et al.  Forecasting nonlinear time series with a hybrid methodology , 2009, Appl. Math. Lett..

[38]  David Horn,et al.  Combined Neural Networks for Time Series Analysis , 1993, NIPS.