INFERENCE IN MEDIAN AR MODELS WITH NONSTATIONARY AND HEAVY-TAILED HETEROSKEDASTIC NOISES
研究了自回归模型中未指定且重尾异方差噪声的估计与推断问题，构建分段局部平稳结构捕捉异质性，提出自加权最小绝对偏差估计量并推导其渐近正态性，通过自助法和残差检验实现可行推断，适用于经济和金融时间序列。
This article studies estimation and inference in the autoregressive (AR) models with unspecified and heavy-tailed heteroskedastic noises. A piece-wise locally stationary structure of the noise is constructed to capture various forms of heterogeneity, without imposing any restrictions on the tail index. The new nonstationary AR model allows for not only time-varying conditional features but also unconditional variance and tail index. This makes it appealing in practice, with wide applications in economics and finance. To obtain a feasible inference, we investigate the self-weighted least absolute deviation estimator and derive its asymptotic normality. Since the asymptotic variance relies on an unobserved density, a bootstrap method is proposed to approximate the limiting distribution. Based on the conditional moment condition, a portmanteau test from residuals is further proposed to detect misspecifications in the proposed model. A simulation study and two applications to time series illustrate our inference procedures.