Abstract: Factor models have been extensively employed in high dimensional time series. However, little is known for the case with the sparse loading matrix. This paper introduces a sparse factor model with an easy-to-implement estimation method, aiming to enhance interpretability and relax the constraints on the dimension p of the time series. In particular, it is shown that under weak conditions, the loading space could be consistently estimated with a convergence rate related to the sparseness of each column in the loading matrix and the eigenvalues used to recover the latent factor and loading matrix. In addition, a randomized sequential test is introduced to determine the number of sparse factors. Simulations and real data analysis on sea surface air pressure and stock portfolios are also provided to illustrate the performance of the proposed method.

Key words and phrases: α-mixing, high dimensional time series, orthogonal projec- tion, sparse factor model.