School of Mathematical Sciences

Bootstrapping M-estimators in GARCH models menu

Bootstrapping M-estimators in GARCH models

K. Mukherjee, Lancaster University
Thu, 01/06/2017 - 16:30
Queens' W316
Seminar series: 

In this talk we discuss a class of M-estimators of parameters in GARCH models. The class of estimators contains least absolute deviation and Huber's estimator as well as the well-known quasi maximum likelihood estimator. For some estimators, the asymptotic normality results are obtained only under the existence of fractional unconditional moment assumption on the error distribution and some mild smoothness and moment assumptions on the score function. Next we analyse the bootstrap approximation of the distribution of M-estimators. It is seen that the bootstrap distribution (given the data) is a consistent estimate (in probability) of the distribution of the M-estimators. We propose an algorithm for the computation of M-estimates which at the same time is software-friendly to compute the bootstrap replicates from the given data. We illustrate our algorithm through simulation study and the analysis of recent financial data.