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

We propose semiparametric model averaging schemes for nonlinear dynamic time series regression models with a very large (ultra) number of covariates including exogenous regressors and auto-regressive lags. Our purpose is to obtain accurate forecasts of a response variable making use of a large number of conditioning variables in a nonparametric way. We propose two semiparametric schemes of dimension reduction among the exogenous regressors and the auto-regressors. (lags of the response variable). 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 significant contribution to estimating the joint multivariate regression function; and thus reduces the dimension of the regressors from a possible exponential rate to a certain polynomial rate, typically smaller than the sample size; we then propose a semiparametric penalised 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 a popular principal component analysis to estimate the latent common factors. We then apply the penalised 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 ultimately determine the optimal combination of the significant marginal regression and auto-regression functions. Under some regularity conditions, we derive some asymptotic properties for these two semiparametric dimension-reduction schemes. Numerical studies including both simulation and an empirical application are provided to illustrate the proposed methodology