Time representation and temporal reasoning plays an important role in time-series analysis and prediction, which involve dealing with varying situations in terms of states of the world evolving with time. Generally speaking, the world in the discourse persists in a given state until some action(s) is carried out, or some event(s) occurs, to change it into another state. This paper presents a framework for prediction and analysis based on time-series of states. It takes a time theory that addresses both points and intervals as primitive time elements on an equal footing as the temporal basis. A state of the world under consideration is defined as a set of time-varying propositions that include properties, facts, actions, events, processes and anything else with Boolean truth-values that are dependent on time. A time-series of states is then defined as a list of states temporally ordered one after another. The framework supports explicit expression of both absolute and relative temporal knowledge. While a formal schema for expressing general time-series of states is given, allowing a time-series of states to be incomplete in various ways, the concept of complete time-series of states is also formally introduced. As the application of the proposed formalism in prediction and time-series analysis, illustrating examples are provided.