Efficient Estimation of a Model with an Autoregressive Signal with White Noise.

摘要

This paper considers the estimation of parameters in the model of X sub t = S sub t + epsilon sub t where the S sub t are generated by a stationary autoregressive model sum from i = o to p of (alpha sub i) (S sub t-i) = eta sub t and the eta sub t and the epsilon sub t are i.i.d. random variables. This paper gives the asymptotic distribution of an approximate maximum-likelihood estimate using only a condition on the fourth-order moment of epsilon sub t and eta sub t and without the assumption of normality. This paper also contains a theorem which shows that under general conditions an estimate given by the second-step in the Newton-Raphson iteration with a consistent estimate as an initial value is second-order efficient.