Though forecasting methods are used in numerous fields, we have seen no work on providing a general theoretical framework to build forecast operators into temporal databases. In this paper, we first develop a formal definition of a forecast operator as a function that satisfies a suite of forecast axioms. Based on this definition, we propose three families of forecast operators called deterministic, probabilistic, and possible worlds forecast operators. Additional properties of coherence, monotonicity, and fact preservation are identified that these operators may satisfy (but are not required to). We show how deterministic forecast operators can always be encoded as probabilistic forecast operators, and how both deterministic and probabilistic forecast operators can be expressed as possible worlds forecast operators. Issues related to the complexity of these operators are studied, showing the relative computational tradeoffs of these types of forecast operators. Finally, we explore the integration of forecast operators with standard relational operators in temporal databases and propose several policies for answering forecast queries.