Adaptive Pointwise Estimation in Time-Inhomogeneous Time-Series Models

This paper offers a new method for estimation and forecasting of the linear and nonlinear time series when the stationarity assumption is violated. Our general local parametric approach particularly applies to general varying-coefficient parametric models, such as AR or GARCH, whose coefficients may arbitrarily vary with time. Global parametric, smooth transition, and changepoint models are special cases. The method is based on an adaptive pointwise selection of the largest interval of homogeneity with a given right-end point by a local change-point analysis. We construct locally adaptive estimates that can perform this task and investigate them both from the theoretical point of view and by Monte Carlo simulations. In the particular case of GARCH estimation, the proposed method is applied to stock-index series and is shown to outperform the standard parametric GARCH model.adaptive pointwise estimation;autoregressive models;conditional heteroscedasticity models;local time-homogeneity

Robust Econometrics

Econometrics often deals with data under, from the statistical point of view, non-standard conditions such as heteroscedasticity or measurement errors and the estimation methods need thus be either adopted to such conditions or be at least insensitive to them. The methods insensitive to violation of certain assumptions, for example insensitive to the presence of heteroscedasticity, are in a broad sense referred to as robust (e.g., to heteroscedasticity). On the other hand, there is also a more specific meaningof the word `robust`, which stems from the field of robust statistics. This latter notion defines robustness rigorously in terms of behavior of an estimator both at the assumed (parametric) model and in its neighborhood in the space of probability distributions. Even though the methods of robust statistics have been used only in the simplest setting such as estimation of location, scale, or linear regression for a long time, they motivated a range of new econometric methods recently, which we focus on in this chapter

Robust estimation of dimension reduction space

Most dimension reduction methods based on nonparametric smoothing are highly sensitive to outliers and to data coming from heavy-tailed distributions.We show that the recently proposed methods by Xia et al.(2002) can be made robust in such a way that preserves all advantages of the original approach.Their extension based on the local one-step M-estimators is sufficiently robust to outliers and data from heavy tailed distributions, it is relatively easy to implement, and surprisingly, it performs as well as the original methods when applied to normally distributed data.