The average of)( ti and oc +2 is
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Abstract
For statistical inference of means of stationary processes, one needs to estimate 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 is a multiple of the spectral density at zero. The classical TAVC estimate which is based on batched means does not allow recursive updates and the required memory complexity is O(n). We propose a faster algorithm which recursively computes the TAVC, thus having memory complexity of order O(1) and the computational complexity scales linearly in n. Under short-range dependence conditions, we establish moment and almost sure convergence of the recursive TAVC estimate. Convergence rates are also obtained.
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The Annals of Applied Probability publishes research papers of the highest quality reflecting the many facets of contemporary applied probability. Primary emphasis is placed on importance and originality. The Annals of Applied Probability has two over-riding criteria for publishing of papers, other than formal correctness and coherence. These are: (a) that the results in the paper should be genuinely applied or applicable; and (b) that the paper should make a serious contribution to the mathematical theory of probability, or in some other sense carry a substantial level of probabilistic innovation, or be likely to stimulate such innovation. Fundamentally, we seek a broad spectrum of papers which intellectually enriches our profession, and which illustrate the ways in which probabilistic thinking has a role in solving real applied problems, interpreted in a wide sense.
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The purpose of the Institute of Mathematical Statistics (IMS) is to foster the development and dissemination of the theory and applications of statistics and probability. The Institute was formed at a meeting of interested persons on September 12, 1935, in Ann Arbor, Michigan, as a consequence of the feeling that the theory of statistics would be advanced by the formation of an organization of those persons especially interested in the mathematical aspects of the subject. The Annals of Statistics and The Annals of Probability (which supersede The Annals of Mathematical Statistics), Statistical Science, and The Annals of Applied Probability are the scientific journals of the Institute. These and The IMS Bulletin comprise the official journals of the Institute. The Institute has individual membership and organizational membership. Dues are paid annually and include a subscription to the newsletter of the organization, The IMS Bulletin. Members also receive priority pricing on all other IMS publications.
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