Closing the GARCH gap: Continuous time GARCH modeling

Time Models

A Simple Asymptotic Analysis of Residual-Based Statistics

What s the asymptotic null distribution of a rank-based serial autocorrelation test applied to residuals of an estimated GARCH model?What s the limiting distribution of estimated ACD parameters applied to the residuals of some first-stage modelling procedure?This paper addresses the often occurring situation in econometrics of applying standard statistics to residuals instead of innovations.The paper provides a simple and unified way of calculating the necessary adjustment in the limiting distribution, be it of tests or estimators. On the technical side, we also provide a novel approach to this problem using Le Cam s theory of convergence of experiments (in this paper restricted to Gaussian shift experiments).The resulting formula is simple and the regularity conditions required fairly minimal.Numerous examples show the strength and wide applicability of our approach.statistics;estimation;ranking

Semiparametric Lower Bounds for Tail Index Estimation

indexation;semiparametric estimation

Semiparametrically Efficient Inference Based on Signs and Ranks for Median Restricted Models

Since the pioneering work of Koenker and Bassett (1978), econometric models involving median and quantile rather than the classical mean or conditional mean concepts have attracted much interest.Contrary to the traditional models where the noise is assumed to have mean zero, median-restricted models enjoy a rich group-invariance structure.In this paper, we exploit this invariance structure in order to obtain semiparametrically efficient inference procedures for these models.These procedures are based on residual signs and ranks, and therefore insensitive to possible misspecification of the underlying innovation density, yet semiparametrically efficient at correctly specified densities.This latter combination is a definite advantage of these procedures over classical quasi-likelihood methods.The techniques we propose can be applied, without additional technical difficulties, to both cross-sectional and time-series models.They do not require any explicit tangent space calculation nor any projections on these.models;regression analysis;econometrics