Supplement: Estimating Structured Vector Autoregressive Model
نویسندگان
چکیده
Consider a vector autoregressive (VAR) model of order d: xt = A1xt−1 + . . .+Adxt−d + t, t = 0,±1,±2, . . . , (1) where xt ∈ R is a random vector, Ai ∈ Rp×p, i = 1, . . . , d are fixed coefficient matrices and t is a vector of zero-mean white noise, i.e., E( t) = 0, E( t t ) = Σ and E( t T t+h) = 0, for h 6= 0. We assume that the noise covariance matrix Σ is positive definite with bounded largest eigenvalue, i.e., Λmin(Σ) > 0 and Λmax(Σ) <∞. The above formulation in (1) can be written compactly as a VAR model of order 1:
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