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A Note on the Predictors of Differenced Sequences
Author(s) -
Peiris M. Shelton
Publication year - 1987
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1987.tb00719.x
Subject(s) - mathematics , invertible matrix , sequence (biology) , degree (music) , set (abstract data type) , mean squared prediction error , value (mathematics) , filter (signal processing) , combinatorics , mean squared error , statistics , computer science , pure mathematics , physics , genetics , acoustics , computer vision , biology , programming language
Summary In this note we consider the problems of optimal linear prediction (o.l.p.) and the minimum mean squared error prediction (m.m.s.e.p.) of a sequence X t , which fits to a stationary and invertible ARMA model through the filter (1 ‐ B s ) d X t = Y t . It is shown that these two predictors are not identical in general from the theoretical point of view. Permitting the degree of differencing d to take any real value, a set of conditions for these commonly applied prediction formulas to be identical is given.