Comparison of multivariate statistical methods for dynamic systems modeling

This is the accepted version of the following article: Barceló, S., Vidal-Puig, S. and Ferrer, A. (2011), Comparison of multivariate statistical methods for dynamic systems modeling. Qual. Reliab. Engng. Int., 27: 107–124, which has been published in final form at http://dx.doi.org/10.1002/qre.1102.In this paper two multivariate statistical methodologies are compared in order to estimate a multi-input multi-output transfer function model in an industrial polymerization process. In these contexts, process variables are usually autocorrelated (i.e. there is time-dependence between observations), posing some problems to classical linear regression models. The two methodologies to be compared are both related to the analyses of multivariate time series: Box-Jenkins methodology and partial least squares time series. Both methodologies are compared keeping in mind different issues, such as the simplicity of the process modeling (i.e. the steps of the identification, estimation and validation of the model), the usefulness of the graphical tools, the goodness of fit, and the parsimony of the estimated models. Real data from a polymerization process are used to illustrate the performance of the methodologies under study. Copyright © 2010 John Wiley & Sons, Ltd.This research was partially supported by the Spanish Government (MICINN) and the European Union (RDE funds) under grant DPI2008-06880-C03-03/DPI.Barceló Cerdá, S.; Vidal Puig, S.; Ferrer, A. (2011). Comparison of multivariate statistical methods for dynamic systems modeling. Quality and Reliability Engineering International. 27(1):107-124. https://doi.org/10.1002/qre.1102S107124271Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (2008). Time Series Analysis. Wiley Series in Probability and Statistics. doi:10.1002/9781118619193Reinsel, G. C. (1997). Elements of Multivariate Time Series Analysis. Springer Series in Statistics. doi:10.1007/978-1-4612-0679-8Wold, S. (1994). Exponentially weighted moving principal components analysis and projections to latent structures. Chemometrics and Intelligent Laboratory Systems, 23(1), 149-161. doi:10.1016/0169-7439(93)e0075-fWise, B. M., & Ricker, N. L. (1993). Identification of finite impulse response models with continuum regression. Journal of Chemometrics, 7(1), 1-14. doi:10.1002/cem.1180070102Dayal, B. S., & MacGregor, J. F. (1996). Identification of Finite Impulse Response Models:  Methods and Robustness Issues. Industrial & Engineering Chemistry Research, 35(11), 4078-4090. doi:10.1021/ie960180eFerrer, A., Aguado, D., Vidal-Puig, S., Prats, J. M., & Zarzo, M. (2008). PLS: A versatile tool for industrial process improvement and optimization. Applied Stochastic Models in Business and Industry, 24(6), 551-567. doi:10.1002/asmb.716Hannan, E. J. (1971). The Identification Problem for Multiple Equation Systems with Moving Average Errors. Econometrica, 39(5), 751. doi:10.2307/1909577Kohn, R. (1979). Identification Results for Armax Structures. Econometrica, 47(5), 1295. doi:10.2307/1911964Chen, C., & Liu, L.-M. (1993). Joint Estimation of Model Parameters and Outlier Effects in Time Series. Journal of the American Statistical Association, 88(421), 284. doi:10.2307/2290724Box, G. E. P., & MacGregor, J. F. (1974). The Analysis of Closed-Loop Dynamic-Stochastic Systems. Technometrics, 16(3), 391. doi:10.2307/1267669Geladi, P., & Kowalski, B. R. (1986). Partial least-squares regression: a tutorial. Analytica Chimica Acta, 185, 1-17. doi:10.1016/0003-2670(86)80028-9Helland, I. S. (1988). On the structure of partial least squares regression. Communications in Statistics - Simulation and Computation, 17(2), 581-607. doi:10.1080/03610918808812681Höskuldsson, A. (1988). PLS regression methods. Journal of Chemometrics, 2(3), 211-228. doi:10.1002/cem.1180020306Wold, S., Albano, C., Dunn, W. J., Edlund, U., Esbensen, K., Geladi, P., … Sjöström, M. (1984). Multivariate Data Analysis in Chemistry. Chemometrics, 17-95. doi:10.1007/978-94-017-1026-8_