双重时序模型矩估计的渐近性:1.样本自协方差(自相关)函数

ASYMPTOTIC PROPERTIES OF MOMENT ESTIMATION FOR A DOUBLY STOCHASTIC MODEL:1.SAMPLE AUTOCOVARIANCE (AUTOCORRELATION) FUNCTION

双重时序模型自提出以来，特别是关于模型的概率性质（如平稳性，遍历性）已有许多讨论，但统计推断方面的文章还很少．作为［9，10］工作的继续，本文及后续文章将讨论矩估计及其大样本性质．首先在本文中，基本的矩估计量（样本自协方差函数及样本自相关国数）的渐近性质对AR（1）－MA（q）模型得到讨论，证明了其渐近正态，并获得了强相合的收敛速度．

Since Tjφstheim (1986) put forward the doubly stochastic model, there have been many works mainly on the probabilistic properties (e.g., stationarity and ergodicity),but has been very little on the statistical inference. In the present and subsequent papers,the moment estimation and its asymptotic properties are focused on for a doubly stochastic AR-MA model as the consequent works of Lu[9,10]. And at first in this present paper,the asymptotic properties of sample autocovariance function and sample autocorrelation function are discussed, for which the asymptotic normality and the a.s. convergence rate are derived.