DOI: https://doi.org/10.15587/1729-4061.2014.21189

A method for building a forecasting model with dynamic weights

Vladyslav Gorbatiuk, Victor Sineglazov, Olena Chumachenko

Abstract



The forecasting task and some of the main problems, that occur while solving it, were examined in the paper. The main existing forecasting methods, that unfortunately do not take into account these problems, were listed together with their short description. We propose a new approach for building the forecasting methods, which considers some of the mentioned problems. Based on this approach, we constructed a new forecasting method, called ‘linear regression with dynamic weights’, which finds concrete values of weights for the input factors depending on the values of the factors themselves. To test the forecasting abilities of the method we used the set of real time series, for which we built a forecasting model using the proposed method, the “ancestor” method – pure linear regression and the group method of data handling. By analyzing the results we show that the new method produced (on average) better forecasting error than the linear regression, and for some time series its error was better than the group method of data handling produced. In a conclusion we suggested some ways for the future improvement of the method


Keywords


time series forecasting; linear regression; Bayesian model averaging; neural networks

Full Text:

PDF

References


Cook, R. D. Influential Observations in Linear Regression [Text] / R. D. Cook // Journal of the American Statistical Association. – 1979. – № 74. – P. 169–174.

Stepashko, V. S. GMDH Algorithms as Basis of Modeling Process Automation after Experimental Data [Text] / V. S. Stepashko // Sov. J. of Automation and Information Sciences. – 1988. – № 21 (4). – Р. 43–53.

Rosenblatt, F. The Perceptron: A Probalistic Model For Information Storage And Organization In The Brain [Text] / F. Rosenblatt // Psychological Review. – 1958. – № 65 (6). – P. 386–408.

Auer, P. A learning rule for very simple universal approximators consisting of a single layer of perceptrons [Text] / P. Auer, B. Harald, M. Wolfgang // Neural Networks. – 2008. – № 21 (5). – P. 786–795.

Elman, J. L. Finding Structure in Time [Text] / J. L. Elman // Cognitive Science. – 1990. – № 14 (2). – P. 179–211.

Benaouda, D. Wavelet-based nonlinear multi-scale decomposition model for electricity load forecasting [Text] / D. Benaouda, F. Murtagh, J. L. Starck, O. Renaud // Neurocomputing. – 2006. – № 70. – P. 139–154.

Akansu, A. N. Wavelet Transforms in Signal Processing: A Review of Emerging Applications [Text] / A. N. Akansu, W. A. Serdijn, I. W. Selesnick // Physical Communication, Elsevier. – 2010. – № 3 (1). – P. 1–18.

Sineglazov, V. An algorithm for solving the problem of forecasting [Text] / V. Sineglazov, E. Chumachenko, V. Gorbatiuk // Aviation. –

– № 17 (1). – P. 9–13.

Cleveland, W. S. Robust Locally Weighted Regression and Smoothing Scatterplots [Text] / W. S. Cleveland // Journal of the American Statistical Association. – 1979. – № 74 (368). – P. 829–836.

Hoeting, J. A. Bayesian Model Averaging: A Tutorial [Text] / J. A. Hoeting, D. Madigan, A. E. Raftery, C. T. Volinsky // Statistical Science. – 1999. – № 14 (4). – P. 382–401.

U.S. General Aviation Aircraft Shipments and Sales [Electronic resource] / Barr Group Aerospace & AeroWeb / Available at: http://www.bga-aeroweb.com/database/Data3/US-General-Aviation-Aircraft-Sales-and-Shipments.xls. – 2014.

Data Sets for Time-Series Analysis [Electronic resource] / Evolutionary and Neural Computation for Time Series Prediction Minisite. – Available at: http://tracer.uc3m.es/tws/TimeSeriesWeb/repo.html - 2005.

Jekabsons, G. GMDH-type Polynomial Neural Networks for Matlab [Electronic resource] / Gints Jekabsons. Regression software and datasets. – Available at: http://www.cs.rtu.lv/jekabsons/ - 2013.

Lendasse, A. Time Series Prediction Competition: The CATS Benchmark [Text] / A. Lendasse, E. Oja, O. Simula, M. Verleysen // International Joint Conference on Neural Networks, Budapest (Hungary), IEEE. – 2004. – P. 1615–1620.

Cook, R. D. (1979). Influential Observations in Linear Regression. Journal of the American Statistical Association, 74, 169–174.

Stepashko, V. S. (1988). GMDH Algorithms as Basis of Modeling Process Automation after Experimental Data. Sov. J. of Automation and Information Sciences, 21 (4), 43–53.

Rosenblatt, F. (1958). The Perceptron: A Probalistic Model For Information Storage And Organization In The Brain. Psychological Review, 65 (6), 386–408.

Auer, P., Harald, B., Wolfgang, M. (2008). A learning rule for very simple universal approximators consisting of a single layer of perceptrons. Neural Networks, 21 (5), 786–795.

Elman, J. L. (1990). Finding Structure in Time. Cognitive Science, 14 (2), 179–211.

Benaouda, D., Murtagh, F., Starck, J. L., Renaud, O. (2006). Waveletbased nonlinear multi-scale decomposition model for electricity load forecasting. Neurocomputing, 70, 139–154.

Akansu, A. N., Serdijn, W. A., Selesnick, I. W. (2010). Wavelet Transforms in Signal Processing: A Review of Emerging Applications. Physical Communication, Elsevier, 3 (1), 1–18.

Sineglazov, V., Chumachenko, E., Gorbatiuk, V. (2013). An algorithm for solving the problem of forecasting, Aviation, 17 (1), 9–13.

Cleveland, W. S. (1979). Robust Locally Weighted Regression and Smoothing Scatterplots. Journal of the American Statistical Association, 74 (368), 829–836.

Hoeting, J. A., Madigan, D., Raftery, A. E., Volinsky, C. T. (1999). Bayesian Model Averaging: A Tutorial. Statistical Science, 14 (4), 382–401.

U.S. General Aviation Aircraft Shipments and Sales [online] (2012). Available at: http://www.bga-aeroweb.com/database/Data3/US-General-Aviation-Aircraft-Sales-and-Shipments.xls.

Data Sets for Time-Series Analysis [online] (2005). Available at: http://tracer.uc3m.es/tws/TimeSeriesWeb/repo.html.

Jekabsons, G. (2010). GMDH-type Polynomial Neural Networks for Matlab. Available at: http://www.cs.rtu.lv/jekabsons/.

Lendasse, A., Oja, E., Simula, O., Verleysen, M. (2004). Time Series Prediction Competition: The CATS Benchmark. International Joint Conference on Neural Networks, Budapest (Hungary), IEEE, 1615–1620.


GOST Style Citations








Copyright (c) 2014 Vladyslav Gorbatiuk, Victor Sineglazov, Olena Chumachenko

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

ISSN (print) 1729-3774, ISSN (on-line) 1729-4061