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Asymptotic Mean‐Square Error of Predicting More than One‐Step Ahead Using the Regression Method
Author(s) -
Bhansali R. J.
Publication year - 1974
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2347051
Subject(s) - statistics , regression , mean squared error , mathematics , regression analysis , mean squared prediction error , square (algebra) , computer science , geometry
Summary We consider the question of linear, least‐squares prediction of the future values of a discrete, stationary autoregressive process from a realization of past values. An expression is given for the asymptotic mean‐square error of predicting more than one‐step ahead when the autoregressive coefficients are estimated from the sample by solving the Yule‐Walker equations. Computer results are given to demonstrate the usefulness of the asymptotic result.