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ASYMPTOTIC INFERENCES FOR AN AR(1) MODEL WITH A CHANGE POINT: STATIONARY AND NEARLY NON‐STATIONARY CASES
Author(s) -
Pang Tianxiao,
Zhang Danna,
Chong Terence TaiLeung
Publication year - 2014
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/jtsa.12055
Subject(s) - mathematics , estimator , monte carlo method , asymptotic distribution , combinatorics , autoregressive model , constant (computer programming) , zero (linguistics) , statistical physics , statistics , physics , linguistics , philosophy , computer science , programming language
This article examines the asymptotic inference for AR(1) models with a possible structural break in the AR parameter β near the unity at an unknown time k 0 . Consider the model y t = β 1 y t − 1 I { t ≤ k 0 } + β 2 y t − 1 I { t > k 0 } + ϵ t , t = 1,2, … , T , where I { ⋅ } denotes the indicator function. We examine two cases: case I | β 1 | < 1, β 2 = β 2 T = 1 − c ∕ T ; and case II β 1 = β 1 T = 1 − c ∕ T , | β 2 | < 1, where c is a fixed constant, and { ϵ t , t ≥ 1} is a sequence of i.i.d. random variables, which are in the domain of attraction of the normal law with zero means and possibly infinite variances. We derive the limiting distributions of the least squares estimators of β 1 and β 2 and that of the break‐point estimator for shrinking break for the aforementioned cases. Monte Carlo simulations are conducted to demonstrate the finite‐sample properties of the estimators. Our theoretical results are supported by Monte Carlo simulations.