SLANTS: Sequential Adaptive Nonlinear Modeling of Time Series

We propose a method for adaptive nonlinear sequential modeling of time series data. Data are modeled as a nonlinear function of past values corrupted by noise, and the underlying nonlinear function is assumed to be approximately expandable in a spline basis. We cast the modeling of data as finding a good fit representation in the linear span of multidimensional spline basis, and use a variant of $l-1$-penalty regularization in order to reduce the dimensionality of representation. Using adaptive filtering techniques, we design our online algorithm to automatically tune the underlying parameters based on the minimization of the regularized sequential prediction error. We demonstrate the generality and flexibility of the proposed approach on both synthetic and real-world datasets. Moreover, we analytically investigate the performance of our algorithm by obtaining both bounds on prediction errors and consistency in variable selection.