The analysis of time series data issued from smart meters has been studied relatively extensively in the electricity domain. Meanwhile, analysis of medium resolution water consumption data collected via smart meters has become possible recently, and the research has tried to develop statistical and machine learning tools in order to respond to different requirements of the domain, e.g., better understanding of water consumption behaviors and prediction of consumption. In the present paper, we propose a new predictive approach based on Non-homogeneous Markov Models in order to learn the dynamics of water consumption behavior and be able to predict future consumption behaviors with a daily time-step based on exogenous covariates such as consumption, climatic factors, calendar, etc. The data used for this purpose are categorical time series, where each series corresponds to a smart meter and each category corresponds to a specific daily consumption behavior. The experiments are performed on a real data set provided by a water utility in France. Prediction results obtained with the proposed model are compared to those provided by two models, namely, the state independent model and homogeneous Markov model. This predictive classification can be helpful for water utilities in order to better manage the water resources and respond to consumer requirements.