NONPARAMETRIC AND NONLINEAR MODELS AND DATA MINING IN TIME-SERIES - ACASE-STUDY ON THE CANADIAN LYNX DATA

Nonparametric regression methods are used as exploratory tools for for mulating, identifying and estimating non-linear models for the Canadia n lynx data, which have attained benchmark status in the time series l iterature since the work of Moran in 1953. To avoid the curse of dimen sionality in the nonparametric analysis of this short series with 114 observations, we confine attention to the restricted class of additive and projection pursuit regression (PPR) models and rely on the estima ted prediction error variance to compare the predictive performance of various (non-) linear models. A PPR model is found to have the smalle st (in-sample) estimated prediction error variance of all the models f itted to these data in the literature. We use a data perturbation proc edure to assess and adjust for the effect of data mining on the estima ted prediction error variances; this renders most models fitted to the lynx data comparable and nearly equivalent. However, on the basis of the mean-squared error of out-of-sample prediction error, the semipara metric model X-1 = 1.08 + 1.37X(t-1) + f(Xt-2) + theta(1) and Tong's s elf-exciting threshold autoregressive model perform much better than t he PPR and other models known for the lynx data.