Asymptotics for the conditional self-weighted M-estimator of GRCA(1) models with possibly heavy-tailed errors

Ke-Ang Fu, Ting Li, Chang Ni, Wenkai He and Renshui Wu ()
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Ke-Ang Fu: Zhejiang Gongshang University
Ting Li: Zhejiang Gongshang University
Chang Ni: Zhejiang Gongshang University
Wenkai He: Zhejiang Gongshang University
Renshui Wu: Sun Yat-sen University

Statistical Papers, 2021, vol. 62, issue 3, No 14, 1407-1419

Abstract: Abstract Consider a generalized random coefficient AR(1) model, $$y_t=\Phi _t y_{t-1}+u_t$$ y t = Φ t y t - 1 + u t , where $$\{(\Phi _t, u_t)^\prime , t\ge 1\}$$ { ( Φ t , u t ) ′ , t ≥ 1 } is a sequences of i.i.d. random vectors, and a conditional self-weighted M-estimator of $$\textsf {E}\Phi _t$$ E Φ t is proposed. The asymptotically normality of this new estimator is established with $$\textsf {E}u_t^2$$ E u t 2 being possibly infinite. Simulation experiments are carried out to assess the performance of the theory and method in finite samples and a real data example is given.

Keywords: Asymptotic normality; Heavy tail; Random coefficient autoregressive model; Self-weighted M-estimation; 62M10; 60F05 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-019-01141-8

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