Title: Asymptotically constant risk estimator of the time-average variance constant
Authors: Chun Yip Yau - Chinese University of Hong Kong (Hong Kong) [presenting]
Kin Wai Chan - Harvard University (United States)
Abstract: Estimation of the asymptotic variance of a time-average, which is known as the time-average variance constant (TAVC), or long run variance, is important for many statistical procedures involving dependent data. However, the estimation of TAVC is difficult as its performance relies heavily on the choice of a bandwidth parameter. Specifically, the optimal choices of bandwidth of all existing estimators depend on the TAVC itself and another unknown parameters which is very difficult to estimate. Thus, the optimal estimation of TAVC is not achievable. By introducing a novel concept of converging kernel, we develop a new class of TAVC estimators in which the optimal bandwidth is free of unknown parameters and hence can be computed easily. Moreover, we prove that the new estimator has a constant risk asymptotically, in contrast to the exploding risk in the existing estimators.