Sequential Adaptive Estimators in Nonparametric Autoregressive Models

On nonergodicity for nonparametric autoregressive models

*Correspondence: [email protected] School of Science, Jiangxi University of Science and Technology, Ganzhou, 341000, China Abstract In this paper, we introduce a class of nonlinear time series models with random time delay under random environment, sufficient conditions for nonergodicity of these models are developed. The so-called Markovnization methods are used, that is, proper supplem...

Properties of Some Sequential Nonparametric Estimators in Some Multivariate Linear Models

Variance bounds for estimators in autoregressive models with constraints

We consider nonlinear and heteroscedastic autoregressive models whose residuals are martingale increments with conditional distributions that fulfill certain constraints. We treat two classes of constraints: residuals depending on the past through some function of the past observations only, and residuals that are invariant under some finite group of transformations. We determine the efficient ...

Weighted Residual-based Density Estimators for Nonlinear Autoregressive Models

This paper considers residual-based and randomly weighted kernel estimators for innovation densities of nonlinear autoregressive models. The weights are chosen to make use of the information that the innovations have mean zero. Rates of convergence are obtained in weighted L1-norms. These estimators give rise to smoothed and weighted empirical distribution functions and moments. It is shown tha...

1121 on Minimax Prediction for Nonparametric Autoregressive Models

We consider the problem of nonparametric prediction for a multi-dimensional functional autore-gression y t = f(y t?1 ; :::; y t?d) + e t on the basis of N observations of y t. In the case when the unknown nonlinear function f belongs to the Barron class, we propose an estimation algorithm which provides approximations of f with expected L 2 accuracy O(N 1=4 ln 1=4 N). We also show that this app...