Kalman-filtering methods for computing information matrices for time-invariant, periodic, and generally time-varying VARMA models and samples

Abstract Under general conditions, the inverse sample information matrix can be used to establish a Cramer-Rao lower bound of the covariance matrix of parameter estimates of a model, and the inverse asymptotic information matrix is the asymptotic covariance matrix of the parameter estimates. The paper does two things. First, it derives a recursive Kalman-filtering method for computing exact sample and asymptotic information matrices for time-invariant, periodic, or generally time-varying Gaussian vector autoregressive moving-average (VARMA) models and samples. Second, it specializes the recursive method to a nonrecursive method for computing exact asymptotic information matrices for time-invariant or periodic VARMA models and samples

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