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ON RISSANEN'S LOWER BOUND ON THE ACCUMULATED MEAN‐SQUARE PREDICTION ERROR
Author(s) -
Kabaila Paul
Publication year - 1987
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1987.tb00442.x
Subject(s) - mathematics , upper and lower bounds , cramér–rao bound , statistics , mean squared error , gaussian , minimum description length , gaussian process , estimation theory , algorithm , mathematical analysis , chemistry , computational chemistry
. Rissanen (1984) presents a lower bound on the accumulated mean square prediction error for a Gaussian ARMA process. Rissanen proves this result using coding theory. In this paper we show that this bound is related to the Cramer‐Rao bound and Fisher's bound on asymptotic variances, for the case of a Gaussian AR process. This provides some insight into Rissanen's lower bound. Analogues of Rissanen's bound, for nonaccumulated prediction error and a Gaussian AR process, are also presented and discussed.