THIRD ORDER ASYMPTOTIC PROPERTIES OF BLUE AND LSE FOR A REGRESSION MODEL WITH ARMA RESIDUAL

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3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)111-114
Number of pages4
JournalJournal of Time Series Analysis
Volume8
Issue number1
DOIs
Publication statusPublished - 1987
Externally publishedYes

Keywords

  • ARMA process
  • BLUE
  • Edgeworth expansion
  • LSE
  • third‐order asymptotic efficiency
  • Times series regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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