In this talk, I will review some recent progress in theory and prac-

tice on semiparametric model averaging schemes for nonlinear dynamic

time series regression modelling 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 information variables in a nonparametric

way. We (my coauthors including Jia Chen, Degui Li and Oliver Lin-

ton) have proposed several semiparametric penalized methods of Model

Averaging MArginal Regression (MAMAR) for the regressors and autore-

gressors either through an initial screening procedure to screen out the

regressors whose marginal contributions are not signi_cant in estimating

the joint multivariate regression function or by imposing an approximate

factor modelling structure on the ultrahigh dimensional exogenous regres-

sors with principal component analysis used to estimate the latent com-

mon factors. In either case, we construct the optimal combination of the

signi_cant marginal regression and autoregression functions to approx-

imate the objective joint multivariate regression function. Asymptotic

properties for these schemes are derived under some regularity conditions.

Empirical applications of the proposed methodology to forecasting the

economic risk, such as ination risk in the UK, will be demonstrated.