A temporal database forecasting algebra

Francesco Parisi*, Amy Sliva, V. S. Subrahmanian

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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, producing an algebra that extends the relational algebra. 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, orthogonality, 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. We explore the integration of different forecast operators with standard relational operators in temporal databases - including extensions of the relational algebra for the probabilistic and possible worlds cases - and propose several policies for answering forecast queries. Instances where these different forecast policies are equivalent have been identified, and can form the basis of query optimization in forecasting. These policies are evaluated empirically using a prototype implementation of a forecast query answering system and several forecast operators.

Original languageEnglish (US)
Pages (from-to)827-860
Number of pages34
JournalInternational Journal of Approximate Reasoning
Issue number7
StatePublished - Sep 2013
Externally publishedYes


  • Forecasting algebra
  • Forecasting queries
  • Predictive databases
  • Temporal algebra
  • Temporal databases

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Artificial Intelligence
  • Applied Mathematics


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