Title: Long-run covariance matrix estimator for high-dimensional time series
Authors: Haotian Xu - University of Geneva (Switzerland) [presenting]
Yuan Ke - University of Georgia (United States)
Abstract: An estimator of long-run covariance matrix estimator for high-dimensional stationary time series is proposed. This estimator can be represented as the sum of autocovariance matrix estimators up to lag $M$. Generalizing the idea of adaptive Huber regression to dependent data, we study the nonasymptotic deviation properties of our estimator under the functional dependence measure. Moreover, in order to be user-friendly in practice, we provide the strategy of deciding the lag $M$ and give the optimal tuning parameters which depend on the sample size, dimensionality, moment and the dependence. Our result allows heavy-tailed marginal distribution and the dimension to be increasing exponentially with the sample size.