(d) Consider the process X, = ,X-1 +€ + 01€-1 + 0ze-2 where . 0, and 0, are model parameters; and e1, e2, .. are independent and identically distributed random variables with mean 0 and variance o. %3D (1) Identify the process/model. (ii) Show that the process is stationary if lol < 1. (iii) Under what conditions on 0, and 0, is the process invertible?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 1E
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(d) Consider the process X, = ,X-1 +€ + 01e-1+ 0ze-2 where . 0, and 0, are model
parameters; and e, e2, . are independent and identically distributed random variables with
mean 0 and variance o.
%3D
(1) Identify the process/model.
(ii) Show that the process is stationary if lol < 1.
(iii) Under what conditions on 0, and 0, is the process invertible?
Transcribed Image Text:a na (d) Consider the process X, = ,X-1 +€ + 01e-1+ 0ze-2 where . 0, and 0, are model parameters; and e, e2, . are independent and identically distributed random variables with mean 0 and variance o. %3D (1) Identify the process/model. (ii) Show that the process is stationary if lol < 1. (iii) Under what conditions on 0, and 0, is the process invertible?
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