Zhu, Ke and Ling, Shiqing (2014): LADEbased inference for ARMA models with unspecified and heavytailed heteroscedastic noises.

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Abstract
This paper develops a systematic procedure of statistical inference for the ARMA model with unspecified and heavytailed heteroscedastic noises. We first investigate the least absolute deviation estimator (LADE) and the selfweighted LADE for the model. Both estimators are shown to be strongly consistent and asymptotically normal when the noise has a finite variance and infinite variance, respectively. The rates of convergence of the LADE and the selfweighted LADE are $n^{1/2}$ which is faster than those of LSE for the AR model when the tail index of GARCH noises is in (0,4], and thus they are more efficient in this case. Since their asymptotic covariance matrices can not be estimated directly from the sample, we develop the random weighting approach for statistical inference under this nonstandard case. We further propose a novel signbased portmanteau test for model adequacy. Simulation study is carried out to assess the performance of our procedure and one real illustrating example is given.
Item Type:  MPRA Paper 

Original Title:  LADEbased inference for ARMA models with unspecified and heavytailed heteroscedastic noises 
Language:  English 
Keywords:  ARMA(p,q) models; Asymptotic normality; Heavytailed noises; G/ARCH noises; LADE; Random weighting approach; Selfweighted LADE; Signbased portmanteau test; Strong consistency. 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General 
Item ID:  59099 
Depositing User:  Dr. Ke Zhu 
Date Deposited:  14 Oct 2014 16:51 
Last Modified:  30 Sep 2019 20:43 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/59099 