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Suppose that the true (unobserved) log price pof an asset follows the model: Pt = Pt-1 + a,, where {at} is sequence of iid N(0, 1) random variables. Suppose that the observed log price p, follows the model: pt = pi +e, where {e} is another sequence of iid N(0, 0.25) random variables and {et) and {a} are independent. Let r₁= pt-pt-1 be the observed log return. Calculate the lag-1 and lag-2 autocorrelations of r,.

Suppose that the true (unobserved) log price pof an asset follows the model: Pt = Pt-1 + a,, where {at} is sequence of iid N(0, 1) random variables. Suppose that the observed log price p, follows the model: pt = pi +e, where {e} is another sequence of iid N(0, 0.25) random variables and {et) and {a} are independent. Let r₁= pt-pt-1 be the observed log return. Calculate the lag-1 and lag-2 autocorrelations of r,.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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Question 3 Suppose that the true (unobserved) log price p of an asset follows the model: Pt = Pt-1 + at, where {at} is sequence of iid N(0, 1) random variables. Suppose that the observed log price p, follows the model: p = Pt+et, where {e} is another sequence of iid N(0, 0.25) random variables and {e} and {a} are independent. Let r=pr-pr-1 be the observed log return. Calculate the lag-1 and lag-2 autocorrelations of r₁.
Transcribed Image Text:Question 3 Suppose that the true (unobserved) log price p of an asset follows the model: Pt = Pt-1 + at, where {at} is sequence of iid N(0, 1) random variables. Suppose that the observed log price p, follows the model: p = Pt+et, where {e} is another sequence of iid N(0, 0.25) random variables and {e} and {a} are independent. Let r=pr-pr-1 be the observed log return. Calculate the lag-1 and lag-2 autocorrelations of r₁.
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