Application of conventional statistical monitoring methods to periodic processes can result in frequent false alarms and/or missed faults due to the non-stationary behavior seen over a period. To address this problem, we propose to identify and use a stochastic state space model that describes the statistical behavior of changes occurring from period to period. This model, when retooled as a periodically time-varying model, can be used for on-line monitoring and estimation with the aid of a Kalman filter. The same model can also be used for inferential estimation of the variables that are difficult or slow to measure on-line. The proposed approach is applied to a simulation benchmark of a waste water treatment process, which exhibits strong diurnal changes in the feed stream, and is compared against the principal component analysis (PCA) and partial least squares (PLS) methods. Copyright (C) 2004 John Wiley Sons, Ltd.