• Bernoulli
  • Volume 18, Number 2 (2012), 678-702.

Estimation in semi-parametric regression with non-stationary regressors

Jia Chen, Jiti Gao, and Degui Li

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In this paper, we consider a partially linear model of the form Yt = Xtτθ0 + g(Vt) + ϵt, t = 1, …, n, where {Vt} is a β null recurrent Markov chain, {Xt} is a sequence of either strictly stationary or non-stationary regressors and {ϵt} is a stationary sequence. We propose to estimate both θ0 and g(⋅) by a semi-parametric least-squares (SLS) estimation method. Under certain conditions, we then show that the proposed SLS estimator of θ0 is still asymptotically normal with the same rate as for the case of stationary time series. In addition, we also establish an asymptotic distribution for the nonparametric estimator of the function g(⋅). Some numerical examples are provided to show that our theory and estimation method work well in practice.

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Bernoulli, Volume 18, Number 2 (2012), 678-702.

First available in Project Euclid: 16 April 2012

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asymptotic theory nonparametric estimation null recurrent time series semi-parametric regression


Chen, Jia; Gao, Jiti; Li, Degui. Estimation in semi-parametric regression with non-stationary regressors. Bernoulli 18 (2012), no. 2, 678--702. doi:10.3150/10-BEJ344.

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Supplemental materials

  • Supplementary material: Proofs of the theorems. We provide this supplemental document in case the reader may want to have a look at the detailed proofs of Theorems 3.1 and 3.2 and Lemma 6.1. The details are available from Chen, Gao and Li [5].