Lugsail lag windows for estimating time-average covariance matrices

Summary Lag windows are commonly used in time series analysis, econometrics, steady-state simulation and Markov chain Monte Carlo to estimate time-average covariance matrices. In the presence of positive correlation underlying process, estimators this matrix almost always exhibit significant negative bias, leading undesirable finite-sample properties. We propose a new family lag specifically designed improve performance by offsetting bias. Any existing window can be adapted into lugsail equivalent with no additional assumptions. use these spectral variance demonstrate their advantages linear regression model autocorrelated heteroskedastic residuals. further employ weighted batch means because computational efficiency on large output. obtain bias results for multivariate significantly weaken mixing condition process. Superior properties demonstrated vector autoregressive process Bayesian logistic model.