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 auto-regressive lags, aiming to obtain accurate 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 significant contribution to estimating the joint multivariate regression function; we then propose a semiparametric penalised method of Model Averaging MArginal Regression ∗Department of Economics and Related Studies, University of York, Heslington, YO10 5DD, UK. E-mail: [email protected] †Department of Mathematics, University of York, Heslington, YO10 5DD, UK. E-mail: [email protected]. ‡Faculty of Economics, Cambridge University, Austin Robinson Building, Sidgwick Avenue, Cambridge, CB3 9DD, UK. E-mail: [email protected]. §Statistical Sciences Research Institute and School of Mathematical Sciences, University of Southampton, Highfield, Southampton, SO17 1BJ, UK. E-mail: [email protected]. Partially supported by the Marie Curie career integration grant of European Commission.