Kernel ridge regression with lagged dependent variable: applications to prediction of internal bond strength in a medium density fiberboard process
Kim, N., Y. S. Jeong, M. K. Jeong, and T. M. Young.  2012.  IEEE Transactions on Systems, Man, and Cybernetics - Part C: Applications and Reviews, 42(6):1011-102.

Medium density fiberboard (MDF) is one of the most popular products in wood composites industry. Kernel-based regression approaches such as the support vector machine for regression have been used to predict the final product quality characteristics of MDF. However, existing approaches for the prediction do not consider the autocorrelation of observations while exploring the nonlinearity of data. To avoid such a problem, this paper proposes a kernel-based regression model with lagged-dependent variables (LDVs) to consider both autocorrelations of response variables and the nonlinearity of data. We will explore the nonlinear relationship between the response and both independent variables and past response variables using various kernel functions. In this case, it will be difficult to apply existing kernel trick because of LDVs. We derive the kernel ridge estimators with LDVs using a new mapping idea so that the nonlinear mapping does not have to be computed explicitly. In addition, the centering technique of the individual mapped data in the feature space is derived to consider an intercept term in kernel ridge regression (KRR) with LDVs. The performances of the proposed approaches are compared with those of popular approaches such as KRR, ordinary least squares (OLS) with LDVs using simulated and real-life datasets. Experimental results show that the proposed approaches perform better than KRR or ridge regression and yield consistently better results than OLS with LDVs, implying that it can be used as a promising alternative when there are autocorrelations of response variables.