Robust Trend Estimation for AR(1) Disturbances

2019

In this paper for the first time the adaptive efficient estimation problem for nonparametric autoregressive models has been studied. First of all, through the Van Trees inequality the sharp bound for the robust quadratic risks, i.e. the Pinsker constant (see, for example , in [19]), in explicit form has been obtained. Then, through the sharp oracle inequalities method developed in [4] for non parametric autoregressions an adaptive efficient model selection procedure is proposed , i.e. such for which the upper bound of its robust quadratic risk coincides with the obtained Pinsker constant. MSC: primary 62G08, secondary 62G0

Journal of Time Series Analysis, 1981

The confidence interval properties of several estimators of the transition parameter, 4, in the first order autoregressive model are examined by a Monte Carlo study. The least squares confidence interval estimator, as well as two forms of a proposed robust confidence interval based on a generalized M-estimator, are examined under two model alternatives to the classical time series approach: the innovations model (the time series is observed 'perfectly') and the additive effects model (the time series is observed plus an added 'effect'). Samples were generated from a number of symmetric distributions, including the Gaussian and a variety of contaminated distributions with mild to heavy contamination. Over a range of outlier models, values of 4 (.25 to .9), and sample sizes (20 to loo), it was found that the GM-estimators possess desirable confidence interval robustness properties in terms of validity and efficiency. In general, the least squares confidence interval is not robust against symmetric heavy-tailed contamination in the innovations model or against the additive effects model.

The Annals of Statistics, 2009

This paper introduces a new class of robust estimates for ARMA models. They are M-estimates, but the residuals are computed so that the e¤ect of one outlier is is limited to the period where it occurs. These estimates are closely related to those based on a robust …lter, but they have two important advantages: they are consistent and the asymptotic theory is tractable. We perform a Monte Carlo where we show that these estimates compare favorable with respect to standard M-estimates and to estimates based on a diagnostic procedure.

2011

This paper reviews recent developments of robust estimation in linear time series models, with short and long memory correlation structures, in the presence of additive outliers. Based on the manuscripts Fajardo et al. (2009) and Lévy-Leduc et al. (2011a), the emphasis in this paper is given in the following directions; the influence of additive outliers in the estimation of a time series, the asymptotic properties of a robust autocovariance function and a robust semiparametric estimation method of the fractional parameter d in ARFIMA(p, d, q) models. Some simulations are used to support the use of the robust method when a time series has additive outliers. The invariance property of the estimators for the first difference in ARFIMA model with outliers is also discussed. In general, the robust long-memory estimator leads to be outlier resistant and is invariant to first differencing.

2010

2012

It is well known that the ordinary least squares (OLS) estimates in the regression model are efficient when the disturbances have mean zero, constant variance and are uncorrelated. In problems concerning time series, it is often the case that the disturbances are, in fact, correlated. It is known that OLS may not be optimal in this context. We consider the robustness of various estimators, including estimated generalized least squares. We found that if the disturbance structure is autoregressive and the dependent variable is nonstochastic and linear or quadratic, the OLS performs nearly as well as its competitors. For other forms of the dependent variable, we have developed rules of thumb to guide practitioners in their choice of estimators.

IEEE Transactions on Signal Processing, 1996

Journal of Econometrics, 2012

This paper studies robust inference in unit root and cointegration models. The analysis covers a range of important inference problems including: testing stationarity against unit roots; testing for structure change in nonstationary regressions; and testing for cointegration. We analyze these inference problems in a uni…ed regression framework, although seperate analysis is given for each speci…c case when it is needed. The proposed inference procedures are constructed based on residuals of robust M-estimations. The limiting behavior of the proposed tests is investigated, and a monte carlo experiment is conducted. The proposed tests are easy to use and have advantages in the presence of non-Gaussian data.

Journal of Nonparametric Statistics, 2004

We develop and test a robust procedure for extracting an underlying signal in form of a time-varying trend from very noisy time series. The application we have in mind is online monitoring data measured in intensive care, where we find periods of relative constancy, slow monotonic trends, level shifts and many measurement artifacts. A procedure is needed which allows a fast and reliable denoising of the data and which distinguishes artifacts from clinically relevant changes in the patient's condition. We use robust regression functionals for local approximation of the trend in a moving time window. For further improving the robustness of the procedure we investigate online outlier replacement by e.g. trimming or winsorization based on robust scale estimators. The performance of several versions of the procedure is compared in important data situations and applications to real and simulated data are given.

Journal of Forecasting, 1994

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.