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The concepts of sparsity, and regularised estimation, have proven useful inmany high-dimensional statistical applications. Dynamic factor models (DFMs)provide a parsimonious approach to modelling high-dimensional time series,however, it is often hard to interpret the meaning of the latent factors. Thispaper formally introduces a class of sparse DFMs whereby the loading matricesare constrained to have few non-zero entries, thus increasing interpretabilityof factors. We present a regularised M-estimator for the model parameters, andconstruct an efficient expectation maximisation algorithm to enable estimation.Synthetic experiments demonstrate consistency in terms of estimating theloading structure, and superior predictive performance where a low-rank factorstructure may be appropriate. The utility of the method is further illustratedin an application forecasting electricity consumption across a large set ofsmart meters.

The Sparse Dynamic Factor Model: A Regularised Quasi-Maximum Likelihood Approach