Estimating nonlinear additive models with nonstationarities and correlated errors
研究了一种适用于时间序列的非参数可加回归模型，包含周期成分、趋势、随机解释变量函数和自回归误差，提出了基于平滑回拟和拟极大似然的估计方法，并建立了渐近理论。
Abstract In this paper, we study a nonparametric additive regression model suitable for a wide range of time series applications. Our model includes a periodic component, a deterministic time trend, various component functions of stochastic explanatory variables, and an AR( p ) error process that accounts for serial correlation in the regression error. We propose an estimation procedure for the nonparametric component functions and the parameters of the error process based on smooth backfitting and quasimaximum likelihood methods. Our theory establishes convergence rates and the asymptotic normality of our estimators. Moreover, we are able to derive an oracle‐type result for the estimators of the AR parameters: Under fairly mild conditions, the limiting distribution of our parameter estimators is the same as when the nonparametric component functions are known. Finally, we illustrate our estimation procedure by applying it to a sample of climate and ozone data collected on the Antarctic Peninsula.