Robust nonlinear regression estimation in null recurrent time series

Semiparametric Regression Estimation in Null Recurrent Nonlinear Time Series

Estimation theory in a nonstationary environment has been very popular in recent years. Existing studies focus on nonstationarity in parametric linear, parametric nonlinear and nonparametric nonlinear models. In this paper, we consider a partially linear model of the form Yt = Xτ t α+g(Vt)+ t, t = 1, · · · , n, where {Vt} is a sequence of β–null recurrent Markov chains, {Xt} is a sequence of ei...

Nonparametric Regression Estimation for Multivariate Null Recurrent Processes

This paper discusses nonparametric kernel regression with the regressor being a d-dimensional β-null recurrent process in presence of conditional heteroscedasticity. We show that the mean function estimator is consistent with convergence rate √ n(T )hd, where n(T ) is the number of regenerations for a β-null recurrent process and the limiting distribution (with proper normalization) is normal. ...

Adaptive estimation in time series regression models

This work develops adaptive estimators for a linear regression model with serially correlated errors. We show that these results continue to hold when the order of the ARMA process characterizing the errors is unknown. The finite sample results are promising, indicating that substantial efficiency gains may be possible for samples as small as 50 observations. We use these estimators to investig...

Variance Estimation in Time Series Regression Models

Uniform Consistency for Nonparametric Estimators in Null Recurrent Time Series

This paper establishes several results for uniform convergence of nonparametric kernel density and regression estimates for the case where the time series regressors concerned are nonstationary null– recurrent Markov chains. Under suitable conditions, certain rates of convergence are also established for these estimates. Our results can be viewed as an extension of some well–known uniform consi...