Let Xt == Yt Y₁ = Zt := = X + nt μ+t-1 Vet with A, ER and where {t} {n} are independent white noise processes with {t} ~ WN(0, 0²), and {n} ~ WN(0,02). Find ex- pressions for the following in terms of model parameters and where possible use notation of Kronecker-Delta functions:

Let Xt == Yt Y₁ = Zt := = X + nt μ+t-1 Vet with A, ER and where {t} {n} are independent white noise processes with {t} ~ WN(0, 0²), and {n} ~ WN(0,02). Find ex- pressions for the following in terms of model parameters and where possible use notation of Kronecker-Delta functions:

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Let
Xt
Yt
Zt
:=
=
=
X + nt
μl + Et-1
Vet
with A, ER and where {t} {n} are independent white noise
processes with {t} ~ WN(0,0²), and {n} ~ WN(0, 2). Find ex-
pressions for the following in terms of model parameters and where
possible use notation of Kronecker-Delta functions:
(b) Autocovariance function of (Yt-et).

Expert Solution

Step 1

From the given information,

$X_{t} : = λ + η_{t}$

$Y_{t} : = μ + ε_{t - 1}$

$Z_{t} : = \nabla ε_{t} = ε_{t} - ε_{t - 1}$

where $λ, μ \in ℝ$

$\{ε_{t}\} ~ W N (0, σ^{2})$ and $\{η_{t}\} ~ W N (0, σ_{η}^{2})$

$\{ε_{t}\} a n d \{η_{t}\}$ are independent white noise processes.

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