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

Yang, Yuxia; Ling, Shiqing

doi:10.1016/j.jeconom.2016.11.009

Cited by 9 publications

(16 citation statements)

References 49 publications

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“…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).…”

Section: Selfmentioning

confidence: 99%

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

Jiang

Zhu

2020

Journal of Econometrics

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This paper considers an augmented double autoregressive (DAR) model, which allows null volatility coefficients to circumvent the over-parameterization problem in the DAR model. Since the volatility coefficients might be on the boundary, the statistical inference methods based on the Gaussian quasi-maximum likelihood estimation (GQMLE) become non-standard, and their asymptotics require the data to have a finite sixth moment, which narrows applicable scope in studying heavy-tailed data. To overcome this deficiency, this paper develops a systematic statistical inference procedure based on the self-weighted GQMLE for the augmented DAR model. Except for the Lagrange multiplier test statistic, the Wald, quasi-likelihood ratio and portmanteau test statistics are all shown to have non-standard asymptotics. The entire procedure is valid as long as the data is stationary, and its usefulness is illustrated by simulation studies and one real example.where u, φ i ∈ R, ω > 0, α i > 0, {η t } is a sequence of independent and identically distributed (i.i.d.) random variables with zero mean and unit variance, and η t is independent of {y s ; s < t}. Model (1.1) was first termed by Ling (2004), and it is a subclass of ARMA-ARCH models in Weiss (1984) and of nonlinear AR models in Cline and Pu (2004), but it is different from Engle's ARCH model if some φ i = 0.

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Section: Selfmentioning

confidence: 99%

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

Jiang

Zhu

2020

Journal of Econometrics

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“…Compared with Yang and Ling (), there are three different aspects at least. First, the SLADE of the threshold of CTAR model has a standard

\sqrt{n}

‐convergence rate and its limiting distribution is still asymptotically normal, which is totally different from that of DTAR model.…”

Section: Introductionmentioning

confidence: 99%

“…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 ().…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Yang

2019

Journal Time Series Analysis

Self Cite

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This note investigates the self-weighted least absolute deviation estimation (SLADE) of a heavy-tailed continuous threshold autoregressive (TAR) model. It is shown that the SLADE is strongly consistent and asymptotically normal. The SLADE is global in the sense that the convergence rate is first obtained before deriving its limiting distribution. Moreover, a test for the continuity of TAR model is considered. A sign-based portmanteau test is developed for diagnostic checking. An empirical example is given to illustrate the usefulness of our method. Combined with the results (Yang and Ling, 2017), a complete asymptotic theory on the SLADE of a heavy-tailed TAR model is established. This enriches asymptotic theory of statistical inference in threshold models.

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Recurrent neural networks integrate multiple graph operators for spatial time series prediction

Peng,

Ding,

Xia

et al. 2023

Appl Intell

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

Cited by 9 publications

References 49 publications

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

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

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

Recurrent neural networks integrate multiple graph operators for spatial time series prediction

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