This paper deals with the problem of global parameter estimation of AD(1, n) where n is a positive integer which is a subclass of affine diffusions introduced by Duffie, Filipovic, and Schachermayer. In general affine models are applied to the pricing of bond and stock options, which is illustrated for the Vasicek, Cox-Ingersoll-Ross and Heston models. Our main results are about the conditional least squares estimation of AD(1, n) drift parameters based on two types of observations : continuous time observations and discrete time observations with high frequency and infinite horizon. Then, for each case, we study the asymptotic properties according to ergodic and non-ergodic cases. This paper introduces as well some moment results relative to the AD(1, n) model.

翻译：本文研究AD(1,n)模型的全局参数估计问题，其中n为正整数，该模型属于Duffie、Filipovic和Schachermayer所引入的仿射扩散过程的一个子类。一般而言，仿射模型被应用于债券与股票期权的定价，这在Vasicek模型、Cox-Ingersoll-Ross模型及Heston模型中均有体现。我们的主要成果涉及基于两类观测数据对AD(1,n)漂移参数进行条件最小二乘估计：连续时间观测数据，以及具有高频采样与无限时间跨度的离散时间观测数据。随后，针对每种情形，我们依据遍历与非遍历两种情况研究了估计量的渐近性质。本文还给出了AD(1,n)模型相关的一些矩量结果。