Robust estimation in long-memory processes under additive outliers

Molinares, Fabio Fajardo; Reisen, Valdério Anselmo; Cribari‐Neto, Francisco

doi:10.1016/j.jspi.2008.12.014

Cited by 38 publications

(44 citation statements)

References 33 publications

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“…Properties of the scale spectrum estimators. The following proposition gives an asymptotic expansion for σ 2 CL,j , σ 2 MAD,j and σ 2 CR,j defined in (17), (18) and (20), respectively. These asymptotic expansions are used for deriving Central Limit Theorems for the different estimators of d. Proposition 1.…”

Section: The Croux and Rousseeuw Estimatormentioning

confidence: 99%

“…We deduce from Proposition 1 and Theorem 6 given and proved in Section 6 the following multivariate Central Limit Theorem for the wavelet coefficient scales. (18) and (20), satisfies the following multivariate Central Limit Theorem…”

Section: The Croux and Rousseeuw Estimatormentioning

confidence: 99%

“…Another technique to robustify the wavelet regression technique has been outlined in [23] which consists in regressing the logarithm of the square of the wavelet coefficients at different scales. [18] proposed a robustified version of the log-periodogram regression estimator introduced in [14]. The method replaces the log-periodogram of the observation by a robust estimator of the spectral density in the neighborhood of the zero frequency, obtained as the discrete Fourier transform of a robust autocovariance estimator defined in [17]; the procedure is appealing and has been found to work well but also lacks theoretical support in the semi-parametric context (note however that the consistency and the asymptotic normality of the robust estimator of the covariance have been discussed in [16]).…”

Section: Introductionmentioning

confidence: 99%

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Central limit theorem for the robust log-regression wavelet estimation of the memory parameter in the Gaussian semi-parametric context

Kouamo¹,

Lévy‐Leduc²,

Moulines³

2013

Bernoulli

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In this paper, we study robust estimators of the memory parameter d of a (possibly) non stationary Gaussian time series with generalized spectral density f . This generalized spectral density is characterized by the memory parameter d and by a function f * which specifies the short-range dependence structure of the process. Our setting is semi-parametric since both f * and d are unknown and d is the only parameter of interest. The memory parameter d is estimated by regressing the logarithm of the estimated variance of the wavelet coefficients at different scales. The two estimators of d that we consider are based on robust estimators of the variance of the wavelet coefficients, namely the square of the scale estimator proposed by [27] and the median of the square of the wavelet coefficients. We establish a Central Limit Theorem for these robust estimators as well as for the estimator of d based on the classical estimator of the variance proposed by [19]. Some Monte-Carlo experiments are presented to illustrate our claims and compare the performance of the different estimators.The properties of the three estimators are also compared on the Nile River data and the Internet traffic packet counts data. The theoretical results and the empirical evidence strongly suggest using the robust estimators as an alternative to estimate the memory parameter d of Gaussian time series.

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Section: The Croux and Rousseeuw Estimatormentioning

confidence: 99%

Section: The Croux and Rousseeuw Estimatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Central limit theorem for the robust log-regression wavelet estimation of the memory parameter in the Gaussian semi-parametric context

Kouamo¹,

Lévy‐Leduc²,

Moulines³

2013

Bernoulli

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“…For a discussion on how outliers affect ARMA parameter estimation, the reader is referred, e.g. to [14], [16], [19], [29], [30] and there is a clear need for robust methods that can, to some extent, resist outliers. First contributions to robust estimation for dependent data were made in the 1980's [31]- [34], and in recent years, research in this area has increased significantly (e.g.…”

Section: Introductionmentioning

confidence: 99%

Bounded Influence Propagation $\tau$ -Estimation: A New Robust Method for ARMA Model Estimation

Muma

Zoubir

2017

IEEE Trans. Signal Process.

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A new robust and statistically efficient estimator for ARMA models called the bounded influence propagation (BIP) τ -estimator is proposed. The estimator incorporates an auxiliary model, which prevents the propagation of outliers. Strong consistency and asymptotic normality of the estimator for ARMA models that are driven by independently and identically distributed (iid) innovations with symmetric distributions are established. To analyze the infinitesimal effect of outliers on the estimator, the influence function is derived and computed explicitly for an AR(1) model with additive outliers. To obtain estimates for the AR(p) model, a robust Durbin-Levinson type and a forward-backward algorithm are proposed. An iterative algorithm to robustly obtain ARMA(p,q) parameter estimates is also presented. The problem of finding a robust initialization is addressed, which for orders p + q > 2 is a non-trivial matter. Numerical experiments are conducted to compare the finite sample performance of the proposed estimator to existing robust methodologies for different types of outliers both in terms of average and of worst-case performance, as measured by the maximum bias curve. To illustrate the practical applicability of the proposed estimator, a real-data example of outlier cleaning for R-R interval plots derived from electrocardiographic (ECG) data is considered. The proposed estimator is not limited to biomedical applications, but is also useful in any real-world problem whose observations can be modeled as an ARMA process disturbed by outliers or impulsive noise.

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“…Zieliński (1999) investigated the median-unbiased estimation of the stationary AR(1) process. Molinares, et al (2009) investigated robust estimation in long-memory processes when the data contains additive outliers.…”

Section: Introductionmentioning

confidence: 99%

Robustness of Several Estimators of the ACF of AR(1) Process With Non-Gaussian Errors

Smadi

Jaber

Alzubi

2014

J. Mod. App. Stat. Meth.

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Robust estimation in long-memory processes under additive outliers

Cited by 38 publications

References 33 publications

Central limit theorem for the robust log-regression wavelet estimation of the memory parameter in the Gaussian semi-parametric context

Central limit theorem for the robust log-regression wavelet estimation of the memory parameter in the Gaussian semi-parametric context

Bounded Influence Propagation $\tau$ -Estimation: A New Robust Method for ARMA Model Estimation

Robustness of Several Estimators of the ACF of AR(1) Process With Non-Gaussian Errors

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