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THIRD ORDER ASYMPTOTIC PROPERTIES OF BLUE AND LSE FOR A REGRESSION MODEL WITH ARMA RESIDUAL
Author(s) -
Taniguchi Masanobu
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.tb00424.x
Subject(s) - mathematics , third order , residual , asymptotic expansion , statistics , mean squared error , regression analysis , square (algebra) , order (exchange) , regression , mathematical analysis , algorithm , geometry , philosophy , theology , finance , economics
Abstract. In this note, we shall investigate third‐order asymptotic properties of BLUE and LSE for a regression model with ARMA residual. In the first place we shall evaluate the asymptotic mean square errors of BLUE and LSE up to third order. For appropriate regression variables (constant or harmonic functions), the asymptotic mean square error of LSE coincides with that of BLUE up to second order. Then we shall evaluate the difference of the asymptotic mean square errors of LSE and BLUE at third order. Secondly we shall show that BLUE is third‐order asymptotically efficient in the sense of the highest probability concentration around the true value in the third‐order Edgeworth expansion.