On the asymptotic normality of autoregressive spectral density estimates for the noise corrupted case

Spectral estimation statistics for noise corrupted autoregressive series--First-order case

“…[n [1], using the cess, that is, {Y N we estimate the covariance asymptotic results of [2] , a closed form expression n n1…”

“…The variance expression for the arbitrary order case is quite complex, thus N-IkI I 'ç' this paper evaluates the estimation variance for the first order AR case and provides numerical n n+IkI ki < N-i results which aid in the interpretation and application of the general variance expression. Due to rk = (5) the complexity of the variance expression in [1] it 0 1k > N-i is not reproduced in this paper, only the reduced version for pl is presented.…”

“…[1], eqns (ii) process X and a noise process w, that is and (12)] with p1 we obtain estimates for the parameters a and a. Using these estimates in (4) YX+w (1) we obtain an estimate for the spectral density, [c ]…”