Self-weighted LAD-based inference for heavy-tailed threshold autoregressive models

Non-standard inference for augmented double autoregressive models with null volatility coefficients

“…When Ey 6 t = ∞, the weight w t is introduced to reduce the effect of leverage points by shrinking their weights on the objective function F n (θ) so that no moment condition of y t is needed but at the sacrifice of efficiency. This idea was initiated by Ling (2005), and it has been adopted in many studies; see, e.g., Ling (2005Ling ( , 2007b, Pan et al (2007), Francq and Zakoïan (2010), Zhu andLing (2011, 2015) and Yang and Ling (2017). In practice, the selection of w t is similar to that of the influence function in Huber (1996).…”

Self‐Weighted Lad‐Based Inference for Heavy‐Tailed Continuous Threshold Autoregressive Models

“…Compared with Yang and Ling (), there are three different aspects at least. First, the SLADE of the threshold of CTAR model has a standard ‐convergence rate and its limiting distribution is still asymptotically normal, which is totally different from that of DTAR model.…”

“…Tong () has looked back on the historical background and motivation that led to the introduction of threshold models in time series analysis as well as a fairly systematic account of the development of these models in the past 30 years or so and promising prospects of threshold models in the future 30 years, and further, Tong () has given some reflections on threshold models. In the last 10 years, asymptotic theory of statistical inference in threshold models has been further developing, see, for example, Caner (), Seo and Linton (), Li and Li (), Li et al, (), Samia and Chan (), Seijo and Sen (), Li and Ling (), Yu, (), Gao et al (), Chan et al, (), Yau et al (), Li and Tong (), Cai et al (), Hansen () and Yang and Ling (). For more related results, see De Gooijer ().…”

“…For heavy‐tailed DTAR models, Yang and Ling () first studied a self‐weighted least absolute deviation estimation (SLADE) and established its asymptotics. Like Yang and Ling (), the CTAR model suffers the same weakness of heavy‐tailedness. In this note, we shall investigate the SLADE of the CTAR model with its asymptotics.…”

“…We emphasize that although Chan and Tsay () also employ VC class to obtain the asymptotic normality of the threshold estimator, their theory does not work for heavy‐tailed CTAR models. Combined with Yang and Ling (), a complete asymptotic theory on the SLADE of heavy‐tailed TAR models is established. This enriches asymptotic theory of statistical inference in threshold models in the literature.…”