Generally, the variations inherited in every single variable measured in dynamic processes consist of autocorrelated, cross-correlated, and unique variations. The filtering of both autocorrelation and cross-correlation from the given data should therefore be given full consideration in modeling dynamic process data as well as implementing fault detection in dynamic processes. Recognition of this issue motivated us to propose a novel dynamic process monitoring method. The proposed method first builds a modified autoregressive (AR) model for every single process variable in a decentralized manner. Second, the resulting decentralized modified AR (DMAR) models are combined into an ensemble formulation, thus facilitating the extraction of the unique variation and the simultaneous elimination of both autocorrelation and cross-correlation from the process variables. The unique variation captured by the residuals in the DMAR models is then modeled and monitored by the standard PCA-based fault detection approach. Finally, the superiority and effectiveness of the proposed DMAR method are validated by comparisons based on two dynamic examples.