A Novel Multilevel-SVD Method to Improve Multistep Ahead Forecasting in Traffic Accidents Domain

Here is proposed a novel method for decomposing a nonstationary time series in components of low and high frequency. The method is based on Multilevel Singular Value Decomposition (MSVD) of a Hankel matrix. The decomposition is used to improve the forecasting accuracy of Multiple Input Multiple Output (MIMO) linear and nonlinear models. Three time series coming from traffic accidents domain are used. They represent the number of persons with injuries in traffic accidents of Santiago, Chile. The data were continuously collected by the Chilean Police and were weekly sampled from 2000:1 to 2014:12. The performance of MSVD is compared with the decomposition in components of low and high frequency of a commonly accepted method based on Stationary Wavelet Transform (SWT). SWT in conjunction with the Autoregressive model (SWT + MIMO-AR) and SWT in conjunction with an Autoregressive Neural Network (SWT + MIMO-ANN) were evaluated. The empirical results have shown that the best accuracy was achieved by the forecasting model based on the proposed decomposition method MSVD, in comparison with the forecasting models based on SWT.

[1]  D. J. Bartholomew,et al.  Time Series Analysis Forecasting and Control , 1971 .

[2]  A. Al-Garni,et al.  Forecasting monthly electric energy consumption in eastern Saudi Arabia using univariate time-series analysis , 1997 .

[3]  David M. Skapura,et al.  Neural networks - algorithms, applications, and programming techniques , 1991, Computation and neural systems series.

[4]  Mark J. Shensa,et al.  The discrete wavelet transform: wedding the a trous and Mallat algorithms , 1992, IEEE Trans. Signal Process..

[5]  Matthias Weidlich,et al.  Traveling time prediction in scheduled transportation with journey segments , 2017, Inf. Syst..

[6]  C. Torrence,et al.  A Practical Guide to Wavelet Analysis. , 1998 .

[7]  Ömer Kaan Baykan,et al.  Predicting direction of stock price index movement using artificial neural networks and support vector machines: The sample of the Istanbul Stock Exchange , 2011, Expert Syst. Appl..

[8]  Biao Leng,et al.  A novel wavelet-SVM short-time passenger flow prediction in Beijing subway system , 2015, Neurocomputing.

[9]  Priya Narayanan,et al.  Trend analysis and ARIMA modelling of pre-monsoon rainfall data for western India , 2013 .

[10]  Sungwon Kim,et al.  Daily water level forecasting using wavelet decomposition and artificial intelligence techniques , 2015 .

[11]  Richard G. J. Flay,et al.  Wind direction forecasting with artificial neural networks and support vector machines , 2015 .

[12]  Kin Keung Lai,et al.  An improved grey neural network model for predicting transportation disruptions , 2016, Expert Syst. Appl..

[13]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[14]  C. Willmott,et al.  A refined index of model performance , 2012 .

[15]  Jochen Köhler,et al.  Prediction of road accidents: A Bayesian hierarchical approach. , 2013, Accident; analysis and prevention.

[16]  J. Hassan,et al.  ARIMA and regression models for prediction of daily and monthly clearness index , 2014 .

[17]  Lida Barba,et al.  Smoothing Strategies Combined with ARIMA and Neural Networks to Improve the Forecasting of Traffic Accidents , 2014, TheScientificWorldJournal.

[18]  P. Krause,et al.  COMPARISON OF DIFFERENT EFFICIENCY CRITERIA FOR HYDROLOGICAL MODEL ASSESSMENT , 2005 .

[19]  Juan de Oña,et al.  Analysis of traffic accident severity using Decision Rules via Decision Trees , 2013, Expert Syst. Appl..

[20]  Blanca Arenas-Ramírez,et al.  Methodological development for selection of significant predictors explaining fatal road accidents. , 2016, Accident; analysis and prevention.

[21]  A. Grossmann,et al.  DECOMPOSITION OF HARDY FUNCTIONS INTO SQUARE INTEGRABLE WAVELETS OF CONSTANT SHAPE , 1984 .

[22]  Eleni I. Vlahogianni,et al.  Optimized and meta-optimized neural networks for short-term traffic flow prediction: A genetic approach , 2005 .

[23]  B. Silverman,et al.  The Stationary Wavelet Transform and some Statistical Applications , 1995 .

[24]  Kenneth Levenberg.  A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[25]  Jingjing Xie,et al.  Air pollutants concentrations forecasting using back propagation neural network based on wavelet decomposition with meteorological conditions , 2016 .

[26]  Pooya Najaf,et al.  Application of an Intelligent Fuzzy Regression Algorithm in Road Freight Transportation Modeling , 2013 .

[27]  Yandong Yang.  Development of the regional freight transportation demand prediction models based on the regression analysis methods , 2015, Neurocomputing.

[28]  Jingsong Yang,et al.  A novel discussion on two long-term forecast mechanisms for hydro-meteorological signals using hybrid wavelet-NN model , 2013 .

[29]  V. Cho.  Tourism Forecasting and its Relationship with Leading Economic Indicators , 2001 .

[30]  Ricardo A. S. Fernandes,et al.  Maximum and minimum stock price forecasting of Brazilian power distribution companies based on artificial neural networks , 2015, Appl. Soft Comput..

[31]  D. Donoho,et al.  Translation-Invariant De-Noising , 1995 .

[32]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

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

[34]  Wei Deng,et al.  New Bayesian combination method for short-term traffic flow forecasting , 2014 .

[35]  George E. P. Box,et al.  Time Series Analysis: Box/Time Series Analysis , 2008 .

[36]  D. Donoho,et al.  Translation-Invariant DeNoising , 1995 .

[37]  Laura Garach,et al.  Bayes classifiers for imbalanced traffic accidents datasets. , 2016, Accident; analysis and prevention.

[38]  Jing Shi,et al.  On comparing three artificial neural networks for wind speed forecasting , 2010 .

[39]  Jianzhou Wang,et al.  Analysis and application of forecasting models in wind power integration: A review of multi-step-ahead wind speed forecasting models , 2016 .