Abstract: Panels of nonlinear time series data are increasingly collected in scientific studies, and a fundamental problem is to study the common dynamic structures of such data. We propose a new model for exploring the common dynamic structure in multivariate nonlinear time series. The basic idea is that the panel of time series are driven by an underlying low-dimensional nonlinear principal component process that is modeled as some nonlinear function of the past lags of the time series. In particular, we consider in some detail the REduced-rank Threshold AutoRegressive (RETAR) model whose nonlinear principal component process is a piecewise linear vector-valued function of past lags of the panel of time series. We propose an estimation scheme for the RETAR model and derive the large sample properties of the estimator. We illustrate the RETAR model using a modern panel of eight Canada lynx series, and demonstrate a classification of lynx series that is broadly similar to that reported by Stenseth et al. (1999), who used a different approach.
Key words and phrases: Common dynamic structure, consistency, maximum likelihood estimation, nonlinear principal component, threshold autoregressive model, weighted least squares.