Limit theory for moderate deviations from a unit root with a break in variance

Cheng Xu and Tianxiao Pang

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 24, 6125-6143

Abstract: Consider the model yt = ρnyt − 1 + ut, t = 1, …, n with ρn = 1 + c/kn and ut = σ1ϵtI{t ⩽ k0} + σ2ϵtI{t > k0}, where c is a non-zero constant, σ1 and σ2 are two positive constants, I{ · } denotes the indicator function, kn is a sequence of positive constants increasing to ∞ such that kn = o(n), and {ϵt, t ⩾ 1} is a sequence of i.i.d. random variables with mean zero and variance one. We derive the limiting distributions of the least squares estimator of ρn and the t-ratio of ρn for the above model in this paper. Some pivotal limit theorems are also obtained. Moreover, Monte Carlo experiments are conducted to examine the estimators under finite sample situations. Our theoretical results are supported by Monte Carlo experiments.

Date: 2018
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DOI: 10.1080/03610926.2017.1406515

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