The concepts of sparsity, and regularised estimation, have proven useful in many 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. This paper formally introduces a class of sparse DFMs whereby the loading matrices are constrained to have few non-zero entries, thus increasing interpretability of factors. We present a regularised M-estimator for the model parameters, and construct an efficient expectation maximisation algorithm to enable estimation. Synthetic experiments demonstrate consistency in terms of estimating the loading structure, and superior predictive performance where a low-rank factor structure may be appropriate. The utility of the method is further illustrated in an application forecasting electricity consumption across a large set of smart meters.

翻译：稀疏性与正则化估计的概念已在许多高维统计应用中显示出其价值。动态因子模型为高维时间序列建模提供了一种简约的方法，然而，潜在因子的含义往往难以解释。本文正式提出了一类稀疏动态因子模型，其中载荷矩阵被约束为仅包含少量非零元素，从而提高了因子的可解释性。我们提出了一种针对模型参数的正则化M估计量，并构建了一种高效的期望最大化算法以实现估计。合成实验表明，该方法在估计载荷结构方面具有一致性，并且在低秩因子结构可能适用时具有优越的预测性能。该方法在跨大型智能电表集的电力消耗预测应用中的实用性得到了进一步验证。