Semiparametric Ultra-High Dimensional Model Averaging of Nonlinear Dynamic Time Series

We propose two semiparametric model averaging schemes for nonlinear dynamic time series regression models with a very large number of covariates including exogenous regressors and autoregressive lags. Our objective is to obtain more accurate estimates and forecasts of time series by using a large number of conditioning variables in a nonparametric way. In the first scheme, we introduce a Kernel Sure Independence Screening (KSIS) technique to screen out the regressors whose marginal regression (or auto-regression) functions do not make a significant contribution to estimating the joint multivariate regression function; we then propose a semiparametric penalized method of Model Averaging MArginal Regression (MAMAR) for the regressors and auto-regressors that survive the screening procedure, to further select the regressors that have significant effects on estimating the multivariate regression function and predicting the future values of the response variable. In the second scheme, we impose an approximate factor modelling structure on the ultra-high dimensional exogenous regressors and use the principal component analysis to estimate the latent common factors; we then apply the penalized MAMAR method to select the estimated common factors and the lags of the response variable that are significant. In each of the two schemes, we construct the optimal combination of the significant marginal regression and auto-regression functions. Asymptotic properties for these two schemes are derived under some regularity conditions. Numerical studies including both simulation and an empirical application to forecasting inflation are given to illustrate the proposed methodology.