Explicit representation of finite predictor coefficients and its applications

Details Explicit representation of finite predictor coefficients and its applications Explicit representation of finite predictor coefficients and its applications

2004-05-04

arxiv.org/abs/math/0405051v4

Annals of Statistics 2006, Vol. 34, No. 2, 973-993

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000000209 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000000209

We consider the finite-past predictor coefficients of stationary time series, and establish an explicit representation for them, in terms of the MA and AR coefficients. The proof is based on the alternate applications of projection operators associated with the infinite past and the infinite future. Applying the result to long memory processes, we give the rate of convergence of the finite predictor coefficients and prove an inequality of Baxter-type.

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