ASYMPTOTICS FOR NONLINEAR TRANSFORMATIONS OF INTEGRATED TIME SERIES
研究了非平稳整合时间序列经非线性变换后生成的随机过程的渐近性质，发现变换函数的指数爆炸会导致样本函数收敛速度依赖于样本路径，并简要展示了这些渐近结果在回归分析中的应用。
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.