Dimension reduction transfer function model
Jin‐Hong Park · Journal of Statistical Computation and Simulation · 2011
The dimension reduction in regression is an efficient method of overcoming the curse of dimensionality in non-parametric regression. Motivated by recent developments for dimension reduction in time series, an empirical extension of central mean subspace in time series to a single-input transfer function model is performed in this paper. Here, we use central mean subspace as a tool of dimension reduction for bivariate time series in the case when the dimension and lag are known and estimate the central mean subspace through the Nadaraya–Watson kernel smoother. Furthermore, we develop a data-dependent approach based on a modified Schwarz Bayesian criterion to estimate the unknown dimension and lag. Finally, we show that the approach in bivariate time series works well using an expository demonstration, two simulations, and a real data analysis such as El Niño and fish Population.