Before revision:  Both simulated and real examples are used to demonstrate the performance of the proposed method in finite samples  .
After revision:  Both simulated and real examples are used to demonstrate the performance of the proposed method in finite samples . We also compare our method with some commonly used ones in the literature regarding the forecast ability of the extracted factors and find that the proposed method performs well in out-of-sample forecasting of a 508-dimensional PM_{2.5 .