4.4 Consider a d-dimensional AR model for a stationary Gaussian random field {Xt} given by sK...
Question:
4.4 Consider a d-dimensional AR model for a stationary Gaussian random field
{Xt} given by
∑
s∈K dsXt−s = ????t, t ∈ ℤd, where {????t} is white noise, and K ⊂ ℤd is a finite set. This framework includes both SARs (Section 4.5) and UARs (Section 4.8). Define a new sequence {as} with terms as = ∑
h∈D dh dh−s, s ∈ D(2)
, where D(2) = {h − s ∶ h,s ∈ D}. Show that this random field can be rewritten as a CAR model (4.31) with coefficients
????s = −as∕a0, s ∈ D(2)
.
Hence, conclude that every AR model can be written as a CAR model.
Hint: Work with the spectral density in both cases.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Question Posted: