SAR1(dgp_params, M_rows, N_cols, dist, dist_ao, margin)SAR1
Notedocblock
A struct to define a first-order simultaneous autoregressive (SAR(1)) model:
\(\qquad Y_{t_1, t_2}=a_1 \cdot Y_{t_1-1, t_2}+a_2 \cdot Y_{t_1, t_2-1}+a_3 \cdot Y_{t_1, t_2+1}+a_4 \cdot Y_{t_1+1, t_2}+\varepsilon_{t_1, t_2}.\)
Yₜ₁,ₜ₂ = a₁ ⋅ Yₜ₁₋₁,ₜ₂ + a₂ ⋅ Yₜ₁,ₜ₂₋₁ + a₃ ⋅ Yₜ₁,ₜ₂₊₁ + a₄ ⋅ Yₜ₁₊₁,ₜ₂ + εₜ₁,ₜ₂
dgp_params::Tuple{a₁::Float64, a₂::Float64, Float64, Float64}: A tuple of the parameters of the DGP. The first element is the parameter a₁, the second element is the parameter a₂, and the third element is the parameter a₃. a₄.M_rows::Int: The number of rows for the final “SOP” matrix. Note that the final spatial matrix (“picture”) equals m + 1.N_cols::Int: The number of columns for the final “SOP” matrix. Note that the final spatial matrix (“picture”) equals n + 1.dist::Distribution: A distribution for . You can use any univariate distribution from theDistributions.jlpackage.dist_ao::Union{Nothing, Distribution}: Nothing or a distribution for additive outliers. For additive outliers you can use any univariate distribution from theDistributions.jlpackage.margin::Int: The margin for the spatial matrix used for initialization.
sar1 = SAR1((0.5, 0.3, 0.2, 0.1), 10, 10, Normal(0, 1), nothing, 20)