Principal component analysis (PCA) has been widely applied for data modeling and process monitoring. However, it is not appropriate to directly apply PCA to data from a dynamic process, since PCA focuses on variance maximization only and pays no attention to whether the components contain dynamics or not. In this paper, a novel dynamic PCA (DiPCA) algorithm is proposed to extract explicitly a set of dynamic latent variables with which to capture the most dynamic variations in the data. After the dynamic variations are extracted, the residuals are essentially uncorrelated in time and static PCA can be applied. The new models generate a subspace of principal time series that are most predictable from their past data. Geometric properties are explored to give insight into the new dynamic model structure. For the purpose of process monitoring, fault detection indices based on DiPCA are developed based on the proposed model. Case studies on simulation data, data from an industrial boiler process, and the Tennessee Eastman process are presented to illustrate the effectiveness of the proposed dynamic models and fault detection methods. (C) 2017 Elsevier Ltd. All rights reserved.