arXiv subjects

Kanchan Mukherjee

Publications and source records attributed to Kanchan Mukherjee.

3 recordsLinked to original sources

arXiv2022

M-estimation in GARCH Models in the Absence of Higher-Order Moments

We consider a class of M-estimators of the parameters of a GARCH (p,q) model. These estimators involve score functions and, for adequate choices of the score functions, are asymptotically normal under milder moment assumptions than the usual quasi maximum likelihood, which makes them more reliable in the presence of heavy tails. We also consider weighted bootstrap approximations of the distributions of these M-estimators and establish their validity. Through extensive simulations, we demonstrate the robustness of these M-estimators under heavy tails and conduct a comparative study of the performance (bias and mean squared errors) of various score functions and the accuracy (confidence interval coverage rates) of their bootstrap approximations. In addition to the GARCH (1, 1) model, our simulations also involve higher-order models such as GARCH~(2, 1) and GARCH~(1,~\!2) which so far have received relatively little attention in the literature. We also consider the case of order-misspecified models. Finally, we use our M-estimators in the analysis of two real financial time series fitted with GARCH (1, 1) or GARCH (2, 1) models.

stat.ME↗

arXiv2020

R-estimators in GARCH models; asymptotics, applications and bootstrapping

The quasi-maximum likelihood estimation is a commonly-used method for estimating GARCH parameters. However, such estimators are sensitive to outliers and their asymptotic normality is proved under the finite fourth moment assumption on the underlying error distribution. In this paper, we propose a novel class of estimators of the GARCH parameters based on ranks, called R-estimators, with the property that they are asymptotic normal under the existence of a more than second moment of the errors and are highly efficient. We also consider the weighted bootstrap approximation of the finite sample distributions of the R-estimators. We propose fast algorithms for computing the R-estimators and their bootstrap replicates. Both real data analysis and simulations show the superior performance of the proposed estimators under the normal and heavy-tailed distributions. Our extensive simulations also reveal excellent coverage rates of the weighted bootstrap approximations. In addition, we discuss empirical and simulation results of the R-estimators for the higher order GARCH models such as the GARCH~($2, 1$) and asymmetric models such as the GJR model.

math.ST↗

arXiv2007

On the design-consistency property of hierarchical Bayes estimators in finite population sampling

We obtain a limit of a hierarchical Bayes estimator of a finite population mean when the sample size is large. The limit is in the sense of ordinary calculus, where the sample observations are treated as fixed quantities. Our result suggests a simple way to correct the hierarchical Bayes estimator to achieve design-consistency, a well-known property in the traditional randomization approach to finite population sampling. We also suggest three different measures of uncertainty of our proposed estimator.

math.ST↗