Maximum Entropy Bootstrap Simulations for Variance Estimation

Abstract

We report a simulation study where we want to consider a fairly simple data generating process (DGP) used in Nordman and Lahiri (JASA, 2012) with a single fixed regressor and regression errors produced by simple AR(1) processes. We focus on the estimation of standard errors of regression coefficients, not the coefficients themselves. We compare confidence intervals by three inference procedures: the usual Chi-square distribution (Chi-sq), the moving blocks bootstrap (MBB) and a newer maximum entropy bootstrap (meboot). Since simulations have a known true standard error, we can assess the coverage and consistency of the meboot. The traditional Chi-sq confidence intervals have very poor coverage, suggesting that they should not be used in the presence of auto-correlated errors. We also consider the advisability of symmetrizing transformation of the ME density by repeating the experiments. We find that symmetrizing offers a slight advantage. Since the meboot appears to be generally superior to others, it can be recommended.

Keywords: auto-correlated errors, symmetrizing transform, moving block bootstrap, simulation, maximum entropy, variance estimation

JEL Classification: C22, C23, C15