ASYMPTOTICS FOR NONLINEAR TRANSFORMATIONS OF INTEGRATED TIME SERIES
ASYMPTOTICS FOR NONLINEAR TRANSFORMATIONS OF INTEGRATED TIME SERIES
复制标题
DOI：
10.1017/s0266466699153015
复制
发表时间：
1999-06
影响因子：
0.8
通讯作者：
Joon Y. Park;P. Phillips
中科院分区：
文献类型：
--
作者：
Joon Y. Park;P. Phillips
针对非平稳积分时间序列的非线性变换产生的随机过程，提出了一个渐近理论。研究了ARIMA时间序列等积分序列的各种非线性函数，得到并分析了这些函数的样本矩的渐近分布。本文考虑的变换包括实际非线性统计分析中使用的各种函数。证明了它们的渐近理论与积分过程和平稳时间序列的渐近理论有很大的不同。例如，当变换函数是指数爆炸时，样本函数的收敛速率是路径相关的。特别是，收敛速度不仅取决于样本的大小，而且取决于实现的样本路径。本文给出了这些渐近性的一些简单应用，以说明非线性变换积分过程对回归的影响。本文中提出的方法对于发展非平稳时间序列的一般非线性回归理论的更大范围的项目是有用的。
An asymptotic theory for stochastic processes generated from nonlinear transformations of nonstationary integrated time series is developed. Various nonlinear functions of integrated series such as ARIMA time series are studied, and the asymptotic distributions of sample moments of such functions are obtained and analyzed. The transformations considered in the paper include a variety of functions that are used in practical nonlinear statistical analysis. It is shown that their asymptotic theory is quite different from that of integrated processes and stationary time series. When the transformation function is exponentially explosive, for instance, the convergence rate of sample functions is path dependent. In particular, the convergence rate depends not only on the size of the sample but also on the realized sample path. Some brief applications of these asymptotics are given to illustrate the effects of nonlinearly transformed integrated processes on regression. The methods developed in the paper are useful in a project of greater scope concerned with the development of a general theory of nonlinear regression for nonstationary time series.