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Throughout, let {et} be a white noise process with constant variance o² 2. Let Xt = 0.5Xt-1- 0.06Xt-2 + et a. Show that this is a weakly stationary AR(2) process ... b. By substituting for Xt-1, Xt-2, in the RHS as necessary, give the coefficients for et, et-1, et-2 and et-3 in the equivalent MA(∞) process. NB: you do not have to substitute further than is necessary. c. Noting that -2 3 1 10.5z+0.06z² 1- 0.2z 1 -0.3z = + derive the MA(∞) representation for Xt, i.e. evaluate X₁ = A(L)¯¹et. d. Compare your results in b and c.

Throughout, let {et} be a white noise process with constant variance o² 2. Let Xt = 0.5Xt-1- 0.06Xt-2 + et a. Show that this is a weakly stationary AR(2) process ... b. By substituting for Xt-1, Xt-2, in the RHS as necessary, give the coefficients for et, et-1, et-2 and et-3 in the equivalent MA(∞) process. NB: you do not have to substitute further than is necessary. c. Noting that -2 3 1 10.5z+0.06z² 1- 0.2z 1 -0.3z = + derive the MA(∞) representation for Xt, i.e. evaluate X₁ = A(L)¯¹et. d. Compare your results in b and c.

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 19E
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Throughout, let {et} be a white noise process with constant variance o²
Transcribed Image Text:Throughout, let {et} be a white noise process with constant variance o²
2. Let Xt = 0.5Xt-1- 0.06Xt-2 + et a. Show that this is a weakly stationary AR(2) process ... b. By substituting for Xt-1, Xt-2, in the RHS as necessary, give the coefficients for et, et-1, et-2 and et-3 in the equivalent MA(∞) process. NB: you do not have to substitute further than is necessary. c. Noting that -2 3 1 10.5z+0.06z² 1- 0.2z 1 -0.3z = + derive the MA(∞) representation for Xt, i.e. evaluate X₁ = A(L)¯¹et. d. Compare your results in b and c.
Transcribed Image Text:2. Let Xt = 0.5Xt-1- 0.06Xt-2 + et a. Show that this is a weakly stationary AR(2) process ... b. By substituting for Xt-1, Xt-2, in the RHS as necessary, give the coefficients for et, et-1, et-2 and et-3 in the equivalent MA(∞) process. NB: you do not have to substitute further than is necessary. c. Noting that -2 3 1 10.5z+0.06z² 1- 0.2z 1 -0.3z = + derive the MA(∞) representation for Xt, i.e. evaluate X₁ = A(L)¯¹et. d. Compare your results in b and c.
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