Robust Estimation of the First-Order Autoregressive Parameter

Denby, Lorraine; Martin, R. Douglas

doi:10.2307/2286743

Cited by 99 publications

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“…The tuning constants are set as CX = 6.0 and C,, = 3.9. Following Denby and Martin (1979), four iterations are calculated with the LS estimates as initial points for the GM estimates with Huber weights. The latter values are then used as starting points for the final GM estimates with Tukey bisquare weights.…”

Section: Monte Carl0 Resultsmentioning

confidence: 99%

“…GENERALIZED-M ESTIMATES Denby and Martin (1979), Miller (1980), and Chang et al (1988) showed that the least squares estimates for linear autoregressive parameters not only lack robustness in terms of variability but also suffer from a severe bias problem when the observations are contaminated by outliers. Therefore it is expected that the existence of additive outliers may also cause similar problems in estimating threshold autoregressive models which are piecewise linear.…”

Section: Through Equations (5)mentioning

confidence: 99%

“…(2) 2, = X, + W I P where 2, is the observed time series, X, follows model (l), 1 i f t = T 1 0 otherwise r p = indicates the location of the outlier, and o represents the magnitude of the outlier. On the other hand, we can also extend the definition of additive outlier in linear time series by Denby and Martin (1979) in which both the number and the location of outliers are determined by a random mechanism:…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On robust estimation of threshold autoregressions

Chan

Cheung

1994

Journal of Forecasting

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We investigate the effects of additive outliers on the least squares (LS) estimation of threshold autoregressive models. The class of generalized-M (GM) estimates for linear time series is modified and applied to non-linear threshold processes. A Monte Car10 experiment is carried out to study the robust properties of these estimates. Their relative forecasting performances are also examined. The results indicate that the GM method is preferable to the LS estimation when the observations are contaminated by additive outliers. A real example is also given to illustrate the proposed method.

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Section: Monte Carl0 Resultsmentioning

confidence: 99%

Section: Through Equations (5)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On robust estimation of threshold autoregressions

Chan

Cheung

1994

Journal of Forecasting

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“…Several robust estimation procedures for autoregressive moving-average model parameters have been proposed along the line of Huber (1964) for location parameters. For example, Denby and Martin (1979) proposed the generalized M-estimates for autoregressive processes. The robustness is achieved by introducing trimmed weights for each summand of score functions.…”

Section: Introductionmentioning

confidence: 99%

Robust Estimation For Periodic Autoregressive Time Series

Shao

2007

Journal Time Series Analysis

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A robust estimation procedure for periodic autoregressive (PAR) time series is introduced. The asymptotic properties and the asymptotic relative efficiency are discussed by the estimating equation approach. The performance of the robust estimators for PAR time-series models with order one is illustrated by a simulation study. The technique is applied to a real data analysis. Copyright 2007 The Author

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“…When the model is an autoregressive moving-average (ARMA) stochastic process, Bustos and Yohai (1986) state several results that show that the additive outliers are more problematic for the estimation of the parameters of an ARMA model. For example, the LS estimators may be severely biased (Denby and Martin, 1979). Innovation outliers occur in an ARMA model when u t has a distribution with tails heavier than those of a normal distribution.…”

Section: Introductionmentioning

confidence: 99%

Robust and powerful serial correlation tests with new robust estimates in ARX models

Duchesne

2005

Journal Time Series Analysis

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We consider robust serial correlation tests in autoregressive models with exogenous variables (ARX). Since the least squares estimators are not robust when outliers are present, a new family of estimators is introduced, called residual autocovariances for ARX (RA-ARX). They provide resistant estimators that are less sensible to abnormal observations in the output variable of the dynamic model. Such 'bad' observations could be due to unexpected phenomena such as economic crisis or equipment failure in engineering, among others. We show that the new robust estimators are consistent and we can consider robust and powerful tests of serial correlation in ARX models based on these estimators. The new one-sided tests of serial correlation are obtained in extending Hong's (1996) approach in a framework resistant to outliers. They are based on a weighted sum of robust squared residual autocorrelations and on any robust and n 1/2 -consistent estimators. Our approach generalizes Li's (1988) test statistic, that can be interpreted as a test using the truncated uniform kernel. However, many kernels deliver a higher power. This is confirmed in a simulation study, where we investigate the finite sample properties of the new robust serial correlation tests in comparison to some commonly used robust and non-robust tests.

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Robust Estimation of the First-Order Autoregressive Parameter

Cited by 99 publications

References 0 publications

On robust estimation of threshold autoregressions

On robust estimation of threshold autoregressions

Robust Estimation For Periodic Autoregressive Time Series

Robust and powerful serial correlation tests with new robust estimates in ARX models

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