Iterated Expectations With Nested Conditioning Sets
The following formulation of the law of iterated expectations plays an important role in many economic and finance models:
where the value of I1 is determined by that of I2. To build intuition, imagine an investor who forecasts a random stock price X based on the limited information set I1. The law of iterated expectations says that the investor can never gain a more precise forecast of X by conditioning on more specific information (I2), if the more specific forecast must itself be forecast with the original information (I1).
This formulation is often applied in a time series context, where Et denotes expectations conditional on only the information observed up to and including time period t. In typical models the information set t + 1 contains all information available through time t, plus additional information revealed at time t + 1. One can then write:
Read more about this topic: Law Of Total Expectation
Famous quotes containing the words iterated, expectations, nested, conditioning and/or sets:
“The customary cry,
‘Come buy, come buy,’
With its iterated jingle
Of sugar-bated words:”
—Christina Georgina Rossetti (1830–1894)
“I always used to suffer a great deal if I let myself get too close to reality since the definitive world of the everyday with its hard edges and harsh light did not have enough resonance to echo the demands I made upon experience. It was as if I never experienced experience as experience. Living never lived up to the expectations I had of it—the Bovary syndrome.”
—Angela Carter (1942–1992)
“A million people—manners free and superb—open
voices—hospitality—the most courageous and friendly young men,
City of hurried and sparkling waters! city of spires and masts!
City nested in bays! my city!”
—Walt Whitman (1819–1892)
“The climacteric marks the end of apologizing. The chrysalis of conditioning has once for all to break and the female woman finally to emerge.”
—Germaine Greer (b. 1939)
“Until, accustomed to disappointments, you can let yourself rule and be ruled by these strings or emanations that connect everything together, you haven’t fully exorcised the demon of doubt that sets you in motion like a rocking horse that cannot stop rocking.”
—John Ashbery (b. 1927)