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ROBUST ESTIMATION IN PARAMETRIC TIME SERIES MODELS UNDER LONG‐ AND SHORT‐RANGE‐DEPENDENT STRUCTURES
Author(s) -
Gao Jiti,
Li Degui,
Lin Zhengyan
Publication year - 2009
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2009.00537.x
Subject(s) - mathematics , estimator , consistency (knowledge bases) , series (stratigraphy) , range (aeronautics) , strong consistency , asymptotic distribution , parametric statistics , mixing (physics) , statistics , asymptotic analysis , estimation , econometrics , paleontology , materials science , geometry , physics , quantum mechanics , composite material , biology , management , economics
Summary This paper studies the asymptotic behaviour of an M‐estimator of regression parameters in the linear model when the design variables are either stationary short‐range dependent (SRD), α‐mixing or long‐range dependent (LRD), and the errors are LRD. The weak consistency and the asymptotic distributions of the M‐estimator are established. We present some simulated examples to illustrate the efficiency of the proposed M‐estimation method.