We consider local least absolute deviation (LLAD) estimation for trend functions of time series with heavy tails which are characterised via a symmetric stable law distribution. The setting includes both causal stable ARMA model and fractional stable ARIMA model as special cases. The asymptotic limit of the estimator is established under the assumption that the process has either short or long ...

In this article we study a fundamental statistical problem: how to optimally pick the objective to be minimized in a parametric regression when we have information about the error distribution. The classical answer to the problem we posed at the beginning, maximum likelihood, was given by Fisher (5) in the specific case of multinomial models and then at succeeding levels of generality by Cramér...

This paper provides a robust statistical approach to nonstationary time series regression and inference. Fully modified extensions of traditional robust statistical procedures are developed that allow for endogeneities in the nonstation-ary regressors and serial dependence in the shocks that drive the regressors and the errors that appear in the equation being estimated. The suggested estima-to...

Nonparametric regression techniques provide an effective way of identifying and examining structure in regression data. The standard approaches to nonparametric regression, such as local polynomial and smoothing spline estimators, are sensitive to unusual observations, and alternatives designed to be resistant to such observations have been proposed as a solution. Unfortunately, there has been ...