Journal ArticleDOI
Asymptotic distributions of some robust scale estimators in explosive AR(1) model
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In this paper, the authors established the asymptotic normality of the median of the absolute residuals and median of absolute differences of pairwise residuals in the first order explosive autoregressive time series.About:
This article is published in Statistics & Probability Letters.The article was published on 2017-07-01. It has received 0 citations till now. The article focuses on the topics: Robust measures of scale & Asymptotic distribution.read more
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Journal ArticleDOI
The limiting distribution of the serial correlation coefficient in the explosive case
TL;DR: In this paper, it is shown that the distribution of the successive $x$'s is not uniquely determined by that of the $u$' s alone, but is determined by a moment generating function, the inversion of which will yield the asymptotic distribution.
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On Asymptotic Distributions of Estimates of Parameters of Stochastic Difference Equations
TL;DR: In this article, it was shown that for any > 1, unless the distribution of the u's is independent, identically distributed with finite variance, the distribution has a limiting Cauchy distribution under the assumption that u's are not necessarily normally distributed.
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Robust Estimation of the First-Order Autoregressive Parameter
Lorraine Denby,R. Douglas Martin +1 more
TL;DR: A class of generalized M-estimates is proposed which has attractive mean-squared-error robustness properties towards both IO and AO type deviations from the Gaussian model.
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M-estimation for autoregressions with infinite variance
TL;DR: In this article, the authors study the problem of estimating autoregressive parameters when the observations are from an AR process with innovations in the domain of attraction of a stable law and show that non-degenerate limit laws exist for M-estimates if the loss function is sufficiently smooth; these results remain valid if location and scale are also estimated.
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General M -estimates for contaminated p th-order autoregressive processes: Consistency and asymptotic normality
TL;DR: In this article, simultaneous estimation of coefficients and a scale parameter of a p th-order autoregressive process (X====== t¯¯¯¯ ) is concerned with simultaneous estimation and validation of coefficients.