Many models of the dynamics of nonlinear time series have large numbers of parameters and tend to overfit. This paper discusses algorithms for selecting the best basis functions from a dictionary for a model of a time series. Selecting the optimal subset of basis functions is typically an NP-hard problem which usually has to be solved by heuristic methods. In this paper, we propose a new heuristic that is a refinement of a previous one. We demonstrate with applications to artificial and real data. The results indicate that the method proposed in this paper is able to obtain better models in most cases.
Nakamura, T., Judd, K., & Mees, A. (2003). Refinements to Model Selection for Nonlinear Time Series. International Journal of Bifurcation and Chaos, 13(5), 1263-1274. https://doi.org/10.1142/S0218127403007205