Concept of statistical causality and local martingales

Abstract

In this paper we consider a statistical concept of causality in continuous time in filtered probability spaces which is based on Granger's definitions of causality. The given causality concept is closely connected to the preservation of the property being a local martingale if the filtration is getting larger. Namely, the local martingale remains unpredictable if the amount of information is increased. We proved that the preservation of this property is equivalent with the concept of causality.

Keywords

• Causality
• filtration
• local martingale
• martingale