Asymptotic normality of pseudo-LS estimator for partly linear autoregression models

Jiti Gao, Hua Liang

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15 Citations (Scopus)

Abstract

Consider the model Yt = βYt-1 + g(Yt-2) + εt for t ≥ 3. Here g is an unknown function, β is an unknown parameter to be estimated and εt are i.i.d. random error with zero 0 and variance σ2 and εt are independent of Ys for all t ≥ 3 and s = 1, 2. A class of asymptotically normal estimators of β are directly obtained based on piecewise polynomial approximator g ̂T(·) of g and the model Yt = βYt-1 + g ̂T(Yt-2) + εt. The asymptotic normality of pseudo-LS (PLS) estimator β ̌T of β and an estimator σ ̌T 2 of σ2 are investigated.

Original languageEnglish
Pages (from-to)27-34
Number of pages8
JournalStatistics and Probability Letters
Volume23
Issue number1
DOIs
Publication statusPublished - 1 Jan 1995

Keywords

  • Asymptotic theory
  • Non-linear time series model
  • Piecewise polynomial

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