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proof of mean square convergence of the sample mean of a stationary process


nvar(ˉXn)=1nni=1nj=1cov(Xi,Xj)=|h|<n(1-|h|n)γ(h)|h|<n|γ(h)|

If γ(n)0 as n then lim, whence var[X¯n]0.
If h=-|γ(h)|< then the dominated Convergence theorem gives

limn|h|<n(1-|h|n)γ(h)=h=-γ(h)

.

Title proof of mean square convergence of the sample meanMathworldPlanetmath of a stationary process
Canonical name ProofOfMeanSquareConvergenceOfTheSampleMeanOfAStationaryProcess
Date of creation 2013-03-22 15:22:19
Last modified on 2013-03-22 15:22:19
Owner georgiosl (7242)
Last modified by georgiosl (7242)
Numerical id 6
Author georgiosl (7242)
Entry type Proof
Classification msc 60G10