Recursive estimation of time-average variance constants

摘要

For statistical inference of means of stationary processes, one needs toestimate their time-average variance constants (TAVC) or long-run variances.For a stationary process, its TAVC is the sum of all its covariances and it isa multiple of the spectral density at zero. The classical TAVC estimate whichis based on batched means does not allow recursive updates and the requiredmemory complexity is O(n). We propose a faster algorithm which recursivelycomputes the TAVC, thus having memory complexity of order O(1) and thecomputational complexity scales linearly in $n$. Under short-range dependenceconditions, we establish moment and almost sure convergence of the recursiveTAVC estimate. Convergence rates are also obtained.