Robust Estimation for ARCH Models

Adaptive density estimation for general ARCH models

Adaptive Estimation in Arch Models

We construct efficient estimators of the identifiable parameters in a regression model when the errors follow a stationary parametric ARCH(P) process. We do not assume a functional form for the conditional density of the errors, but do require that it be symmetric about zero. The estimators of the mean parameters are adaptive in the sense of Bickel [2]. The ARCH parameters are not jointly ident...

Robust Estimation in Linear Regression with Molticollinearity and Sparse Models

‎One of the factors affecting the statistical analysis of the data is the presence of outliers‎. ‎The methods which are not affected by the outliers are called robust methods‎. ‎Robust regression methods are robust estimation methods of regression model parameters in the presence of outliers‎. ‎Besides outliers‎, ‎the linear dependency of regressor variables‎, ‎which is called multicollinearity...

Robust Estimation for Arma Models

This paper introduces a new class of robust estimates for ARMA models. They are M-estimates, but the residuals are computed so the effect of one outlier is limited to the period where it occurs. These estimates are closely related to those based on a robust filter, but they have two important advantages: they are consistent and the asymptotic theory is tractable. We perform a Monte Carlo where ...

Pseudo-maximum Likelihood Estimation of Arch(∞) Models

Strong consistency and asymptotic normality of the Gaussian pseudo-maximum likelihood estimate of the parameters in a wide class of ARCH(∞) processes are established. The conditions are shown to hold in case of exponential and hyperbolic decay in the ARCH weights, though in the latter case a faster decay rate is required for the central limit theorem than for the law of large numbers. Particula...