A two-step estimating approach for heavy-tailed AR models with nonzero median GARCH-type noises

原文摘要

This paper develops a novel two-step estimating procedure for heavy-tailed AR models with nonzero median GARCH-type noises, allowing for time-varying volatility. We first establish the self-weighted quantile regression estimator (SQE) across all quantile levels τ∈(0,1) for the AR parameters θ0. We show that the SQE, less a bias, converges weakly to a Gaussian process at a rate of n−1/2. The bias is zero if and only if τ equals τ0, the probability that the noise is less than zero. Based on the SQE, we propose an approach to estimate τ0 in the second step and feed the estimated τ0 back into the SQE to estimate θ0. Both the estimated τ0 and θ0 are shown to be consistent and asymptotically normal. A random weighting bootstrap method is developed to approximate the complex distribution. The problem we study is nonstandard because τ0 may not be identifiable in conventional quantile regression, and the usual methods cannot verify the existence of the SQE bias. Unlike existing procedures for heavy-tailed time series, our method does not require prior information about the symmetry, tail index, or the parametric form of the noise, nor does it require classical identification conditions, such as zero-mean or zero-median.

摘要来源：Crossref