  We propose a novel approach for time series forecasting with many predictors,
referred to as the GO-sdPCA, in this paper. The approach employs a variable
selection method known as the group orthogonal greedy algorithm and the
high-dimensional Akaike information criterion to mitigate the impact of
irrelevant predictors. Moreover, a novel technique, called peeling, is used to
boost the variable selection procedure so that many factor-relevant predictors
can be included in prediction. Finally, the supervised dynamic principal
component analysis (sdPCA) method is adopted to account for the dynamic
information in factor recovery. In simulation studies, we found that the
proposed method adapts well to unknown degrees of sparsity and factor strength,
which results in good performance even when the number of relevant predictors
is large compared to the sample size. Applying to economic and environmental
studies, the proposed method consistently performs well compared to some
commonly used benchmarks in one-step-ahead out-sample forecasts.
