Regularized multivariable grey model for stable grey coefficients estimation

Recently, the convolution integral-based multivariable grey model (GMC(1, N)) has attracted considerable interest due to its significant performance in time series forecasting. However, this promising technique may occasionally confront ill-posed problem, which is a plague ignored by most researchers. In this paper, a regularized GMC(1, N) framework (R-GMC(1, N)) is proposed to estimate the grey coefficients in case there exists potential ill-posed problem. More specifically, we adopt two state-of-the-art regularization methods, i.e. the Tikhonov regularization (TR) and truncated singular value decomposition (TSVD), together with two regularization parameters detection methods, i.e. L-curve (LC) and generalized cross-validation (GCV), to identify the stable solutions. Numerical simulations on industrial indicators of China demonstrate that our methods yield more accurate forecast results than the existing GMC(1, N).