Innovation Outliers Research Articles

An outlier robust unit root test with an application to the extended Nelson-Plosser data

This paper considers unit root tests based on robust estimators with a high breakdown point and high efficiency. The asymptotic distribution of these tests is derived. Critical values for the test are obtained via simulation. It is found that the size of the classical OLS based Dickey-Fuller test breaks down if the time series contains additive outliers For innovative outliers the size of the robust test is less stable, while its size-adjusted power properties are better. An example is provided by applying the robust tests to the extended Nelson-Plosser data. For four series the null hypothesis of nonstationarity is rejected.

Robust estimation iin time series: an approximation to the gaussian sum filter

This paper proposes a filter which can track the level of a time series robustly and adapt well to step jumps. The filter, called the approximate Gaussian sum filter (AGSF), is derived from the Gaussian sum filter by collapsing the terms in the normal mixtures. Besides producing one-step ahead forecasts robust towards additive and innovation outliers, the filter also estimates the scale parameters in the local level model separately from the variability caused by contamination. Simulation results show that the AGSF produces robust estimates of the hyperparameters regardless of the underlying distributions of the error terms. An example is included to illustrate the robust tracking of the series level by the AGSF as compared with the Kalman filter and an additive outlier filter.

Computation of Certain Minimum Distance Estimators in AR[k] Model

This article gives sufficient conditions that guarantee the existence of minimizers of special classes of functions. Using these results, a certain dass of minimum distance (MD) estimators of the autoregressive parameters is shown to exist under the additive and innovative outliers; that is, autoregression (AO and IO) models. Through simulations, a certain subclass of MD estimators is shown to perform as good as or in some cases even better than other classical estimators like GM and functional least square estimators under the IO and AO models. Simulation results also show that MD estimators are robust against AO's.

Detecting Level Shifts in Time Series

This article demonstrates the difficulty that traditional outlier detection methods, such as that of Tsay, have in identifying level shifts in time series. Initializing the outlier/level-shift search with an estimated autoregressive moving average model lowers the power of the level-shift detection statistics. Furthermore, the rule employed by these methods for distinguishing between level shifts and innovation outliers does not work well in the presence of level shifts. A simple modification to Tsay's procedure is proposed that improves the ability to correctly identify level shifts. This modification is relatively easy to implement and appears to be quite effective in practice.

Identification of pulses in hormone time series using outlier detection methods.

The identification of discrete hormonal secretory pulses is of critical importance in clinical endocrinology. Pulses are defined as sudden increases in hormone concentration followed by exponential decay. We propose a model-based iterative procedure for pulse detection in pulsatile hormone time series. Our model is seen to be analogous to the model for innovation outliers in autoregressive series, and outlier detection techniques for pulse identification are adapted to the endocrine context. An original feature of the procedure is that it distinguishes between true pulses and gross observation outliers in the series. Simulation experiments are used to investigate the behaviour of the method under physiologically or clinically relevant circumstances. Five experimental endocrine series from rhesus monkeys, where the times of the pulses are known from the concomitant recording of the electrical activity of the hypothalamus, are analysed.

A practical method for outlier detection in autoregressive time series modelling

A practical method is developed for outlier detection in autoregressive modelling. It has the interpretation of a Mahalanobis distance function and requires minimal additional computation once a model is fitted. It can be of use to detect both innovation outliers and additive outliers. Both simulated data and real data re used for illustration, including one data set from water resources.

Partially adaptive estimation of ARMA time series models

This paper presents a new partially adaptive estimator of ARMA models which includes least absolute deviation (LAD or L 1), least squares, L p , and ‘optimal’ L p as special or limiting cases. This estimator is based upon a generalized t(GT) distribution for the residuals. The GT distribution has a mixture interpretation based on an innovative outlier framework, and results in an estimator with a bounded ψ-function for finite ‘degrees of freedom.’ Joint estimation of distributional parameters and ARMA parameters allows the estimation technique to ‘adjust’ or ‘adapt’ to the data type and provides a natural way to test for normality of residuals. Monte Carlo simulations compare the performance of these estimators across different distributional assumptions including a ‘contaminated’ normal. The partially adaptive estimators perform well across diverse data types including the innovative outlier and ‘contaminated normal’ models. The distributions of corresponding Q statistics and likelihood ratio statistics are considered.