5. State space models Consider the model T₁ = Tt−1 + €t S₁ = 0.8S-4+ Nt Y₁ = T₁ + S₁ + V₂ where (+) Y₁,..., Y. ~ WN(0,σ²), nt ~ WN(0,σ2), and (V) ~ WN(0,0). We observe data a. Write the model in the standard (matrix) form of a linear Gaussian state space model. b. Does lim+++∞ Var (St - St|n) exist? If so, what is its value? c. Does lim∞ Var(T₁ — Ît\n) exist? If so, what is its value?
5. State space models Consider the model T₁ = Tt−1 + €t S₁ = 0.8S-4+ Nt Y₁ = T₁ + S₁ + V₂ where (+) Y₁,..., Y. ~ WN(0,σ²), nt ~ WN(0,σ2), and (V) ~ WN(0,0). We observe data a. Write the model in the standard (matrix) form of a linear Gaussian state space model. b. Does lim+++∞ Var (St - St|n) exist? If so, what is its value? c. Does lim∞ Var(T₁ — Ît\n) exist? If so, what is its value?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 10RE
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Transcribed Image Text:5. State space models
Consider the model
T₁ = Tt−1 + €t
S₁ = 0.8S-4+ Nt
Y₁ = T₁ + S₁ + V₂
where (+)
Y₁,..., Y.
~
WN(0,σ²), nt ~
WN(0,σ2), and (V)
~
WN(0,0). We observe data
a. Write the model in the standard (matrix) form of a linear Gaussian state space model.
b. Does lim+++∞ Var (St - St|n) exist? If so, what is its value?
c. Does lim∞
Var(T₁ — Ît\n) exist? If so, what is its value?
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