  In this paper, we propose a new nonparametric estimator of time-varying
forecast combination weights. When the number of individual forecasts is small,
we study the asymptotic properties of the local linear estimator. When the
number of candidate forecasts exceeds or diverges with the sample size, we
consider penalized local linear estimation with the group SCAD penalty. We show
that the estimator exhibits the oracle property and correctly selects relevant
forecasts with probability approaching one. Simulations indicate that the
proposed estimators outperform existing combination schemes when structural
changes exist. Two empirical studies on inflation forecasting and equity
premium prediction highlight the merits of our approach relative to other
popular methods.
