On the asymptotic joint distribution of the sum and maximum of stationary normal random variables

Let X 1 , X 2 , ·· ·be stationary normal random variables with ρ n = cov( X 0 , X n ). The asymptotic joint distribution of and is derived under the condition ρ n log n → γ [0,∞). It is seen that the two statistics are asymptotically independent only if γ = 0.