The trajectory patterns of a moving object in a spatio-temporal domain offers varied information in terms of the management of the data generated from the movement. A trajectory data warehouse is a data repository for the data and information of trajectory objects and their associated spatial objects for defined temporal periods. The query results of trajectory objects from the data warehouse are usually not enough to answer certain trend behaviours and meaningful inferences without the associated semantic information of the trajectory object or the geospatial environment within a specified purpose or context. This paper formulates and designs a generic ontology modelling framework that serves as the background model platform for the design of a semantic data warehouse for trajectories. This semantic trajectory data warehouse can be adaptable for trajectory data processing and analytics on any chosen spatio-temporal application domain. The methodology underpins on higher granularity of data as a result of pre-processed and transformed ETL data so as to offer efficient semantic inference to the underlying trajectory data. Moreover, the approach outlines the thematic dimensions that serve as necessary entities for extracting semantic information. Additionally, the modelling approach offers a design platform for effective predictive trend analysis and knowledge discovery in the trajectory dynamics and data processing for moving objects.