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(a) Let {et} be a zero-mean, unit-variance white noise process. Consider a process that begins at time t=0 and is defin
Posted: Thu Jul 14, 2022 4:51 pm
by answerhappygod
- A Let Et Be A Zero Mean Unit Variance White Noise Process Consider A Process That Begins At Time T 0 And Is Defin 1 (58.42 KiB) Viewed 33 times
(a) Let {et} be a zero-mean, unit-variance white noise process. Consider a process that begins at time t=0 and is defined recursively as follows. Let Y0=c1e0 and Y1=c2Y0+e1. Then let Yt=φ1Yt−1+φ2Yt−2+et for t>1 as in an AR(2) process. Show that the process mean is zero. (5 marks) (b) Suppose that {Yt} is generated according to Yt=10+et−21et−1+41et−2, with et∼N(0,1). (i) Identify the model Yt. (2 marks) (ii) Find the mean and covariance functions for {Yt}. Is {Yt} stationary? (2+5+1 marks) (iii) Find the mean and covariance functions for {∇Yt}. Is {∇Yt} stationary? (2+5+1 marks) (vi) Determine ρ1 and ρ2. (6 marks) (v) Using (vi) or otherwise, determine ϕ11 and ϕ22. (4 marks)