Conditional Expectation
It is common in stochastic processes to care about the expected value of a variable given a previous information set. Let be all information that is common knowledge at time t (this is often subscripted below the expectation operator); then the expected value of the realisation of X, j time-steps in the future, can be written equivalently as:
With these time-dependent conditional expectations, there is the need to distinguish between the backshift operator (B) that only adjusts the date of the forecasted variable and the Lag operator (L) that adjusts equally the date of the forecasted variable and the information set:
Read more about this topic: Lag Operator
Famous quotes containing the words conditional and/or expectation:
“Computer mediation seems to bathe action in a more conditional light: perhaps it happened; perhaps it didn’t. Without the layered richness of direct sensory engagement, the symbolic medium seems thin, flat, and fragile.”
—Shoshana Zuboff (b. 1951)
“The expectation that every neurotic phenomenon can be cured may, I suspect, be derived from the layman’s belief that the neuroses are something quite unnecessary which have no right whatever to exist. Whereas in fact they are severe, constitutionally fixed illnesses, which rarely restrict themselves to only a few attacks but persist as a rule over long periods throughout life.”
—Sigmund Freud (1856–1939)