We prove moderate deviations principles for 1) unbounded additive functionals of the form S n = n j=1 g(X (p) j−1 ), where (X n ) n∈N is a stable R d -valued functional autoregressive model of order p with white noise, and g is an R q -valued Lipschitz function of order (r, s); 2) the error of the least squares estimator (LSE) of the matrix θ in an R d -valued regression model X n = θ t φ n−1 + n , where ( n ) is a "generalized Gaussian" noise. We apply these results to study the error of the

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... E for a stable R d -valued linear autoregressive model of order p.