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Title: Semiparametric Ultra-High Dimensional Model Averaging of Nonlinear DynamicTime Series Authors:  Jia Chen - University of York (United Kingdom) [presenting]
Degui Li - University of York (United Kingdom)
Oliver Linton - University of Cambridge (United Kingdom)
Zudi Lu - University of Southampton (United Kingdom)
Abstract: We propose two semiparametric model averaging schemes for nonlinear dynamic time series regression models with a very large number of covariates. Our objective is to obtain accurate estimates and forecasts of time series nonparametrically. In the first scheme we use a Kernel Sure Independence Screening (KSIS) technique to screen out insignificant regressors; we then use a semiparametric penalized method of Model Averaging MArginal Regression (MAMAR) for the regressors that have survived the screening procedure, to further select 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 significant common factors and lags of the response variable. In each of the two schemes, we construct the optimal combination of the significant marginal regression and auto-regression functions. Asymptotic and numerical studies of the proposed methods are provided.