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We study the problem of intervention effects generating various types of outliers in a linear count time series model. This model belongs to the class of observation driven models and extends the class of Gaussian linear time series models within the exponential family framework. Studies about effects of covariates and interventions for count time series models have largely fallen behind due to the fact that the underlying process, whose behavior determines the dynamics of the observed process, is not observed. We suggest a computationally feasible approach to these problems, focusing especially on the detection and estimation of sudden shifts and outliers. To identify successfully such unusual events we employ the maximum of score tests, whose critical values in finite samples are determined by parametric bootstrap. The usefulness of the proposed methods is illustrated using simulated and real data examples.

Tests for shift detection in locally-stationary autoregressive time series are constructed which resist contamination by a substantial amount of outliers. Tests based on a comparison of local medians standardized by a highly robust estimate of the variability show reliable performance in a broad variety of situations if the thresholds are adjusted for possible autocorrelations. Robuste Tests zur Erkennung von Sprüngen in lokalstationären autoregressiven Zeitreihen werden konstruiert mit dem Ziel, auch bei erheblicher Ausreißerkontamination zuverlässig zu arbeiten. Ein Vergleich lokaler Mediane standardisiert mit einem robusten Skalenschätzer erweist sich bei Verwendung ausreichend großer kritischer Werte als besonders zuverlässig in relevanten Szenarien.

Abrupt shifts in the level of a time series represent important information and should be preserved in statistical signal extraction. We investigate rules for detecting level shifts that are resistant to outliers and which work with only a short time delay. The properties of robustified versions of the t-test for two independent samples and its non-parametric alternatives are elaborated under different types of noise. Trimmed t-tests, median comparisons, robustified rank and ANOVA tests based on robust scale estimators are compared.

Current alarm systems on intensive care units create a very high rate of false positive alarms because most of them simply compare the physiological measurements to fixed thresholds. An improvement can be expected when the actual measurements are replaced by smoothed estimates of the underlying signal. However, classical filtering procedures are not appropriate for signal extraction as standard assumptions, like stationarity, do no hold here: the measured time series often show long periods without change, but also upward or downward trends, sudden shifts and numerous large measurement artefacts. Alternative approaches are needed to extract the relevant information from the data, i.e. the underlying signal of the monitored variables and the relevant patterns of change, like abrupt shifts and trends. This article reviews recent research on filter based online signal extraction methods which are designed for application in intensive care.

Robustified rank tests, applying a robust scale estimator, are investigated for reliable and fast shift detection in time series. The tests show good power for sufficiently large shifts, low false detection rates for Gaussian noise and high robustness against outliers. Wilcoxon scores in combination with a robust and efficient scale estimator achieve good performance in many situations.

We analyze multivariate binary time series using a mixed parameterization in terms of the conditional expectations given the past and the pairwise canonical interactions among contemporaneous variables. This allows consistent inference on the influence of past variables even if the contemporaneous associations are misspecified. Particularly, we can detect and test Granger non-causalities since they correspond to zero parameter values.

We discuss robust filtering procedures for signal extraction from noisy time series. Particular attention is paid to the preservation of relevant signal details like abrupt shifts. moving averages and running medians are widely used but have shortcomings when large spikes (outliers) or trends occur. Modifications like modified trimmed means and linear median hybrid filters combine advantages of both approaches, but they do not completely overcome the difficulties. Better solutions can be based on robust regression techniques, which even work in real time because of increased computational power and faster algorithms. Reviewing previous work we present filters for robust signal extraction and discuss their merits for preserving trends, abrupt shifts and local extremes as well as for the removal of outliers.

We propose weighted repeated median filters and smoothers for robust non-parametric regression in general and for robust signal extraction from time series in particular. The proposed methods allow to remove outlying sequences and to preserve discontinuities (shifts) in the underlying regression function (the signal) in the presence of local linear trends. Suitable weighting of the observations according to their distances in the design space reduces the bias arising from non-linearities. It also allows to improve the efficiency of (unweighted) repeated median filters using larger bandwidths, keeping their properties for distinguishing between outlier sequences and long-term shifts. Robust smoothers based on weighted L1- regression are included for the reason of comparison.

We discuss moving window techniques for fast extraction of a signal comprising monotonic trends and abrupt shifts from a noisy time series with irrelevant spikes. Running medians remove spikes and preserve shifts, but they deteriorate in trend periods. Modified trimmed mean filters use a robust scale estimate such as the median absolute deviation about the median (MAD) to select an adaptive amount of trimming. Application of robust regression, particularly of the repeated median, has been suggested for improving upon the median in trend periods. We combine these ideas and construct modified filters based on the repeated median offering better shift preservation. All these filters are compared w.r.t. fundamental analytical properties and in basic data situations. An algorithm for the update of the MAD running in time O(log n) for window width n is presented as well.

In intensive care, time series of vital parameters have to be analysed online, i.e. without any time delay, since there may be serious consequences for the patient otherwise. Such time series show trends, slope changes and sudden level shifts, and they are overlaid by strong noise and many measurement artefacts. The development of update algorithms and the resulting increase in computational speed allows to apply robust regression techniques to moving time windows for online signal extraction. By simulations and applications we compare the performance of least median of squares, least trimmed squares, repeated median and deepest regression for online signal extraction.

Standard median filters preserve abrupt shifts (edges) and remove impulsive noise (outliers) from a constant signal but they deteriorate in trend periods. FIR median hybrid (FMH) filters are more flexible and also preserve shifts, but they are much more vulnerable to outliers. Application of robust regression methods, in particular of the repeated median, has been suggested for removing subsequent outliers from a signal with trends. A fast algorithm for updating the repeated median in linear time using quadratic space is given in Bernholt and Fried (2003). We construct repeated median hybrid filters to combine the robustness properties of the repeated median with the edge preservation ability of FMH filters. An algorithm for updating the repeated median is presented which needs only linear space. We also investigate analytical properties of these filters and compare their performance via simulations.

We discuss the robust estimation of a linear trend if the noise follows an autoregressive process of first order. We find the ordinary repeated median to perform well except for negative correlations. In this case it can be improved by a Prais-Winsten transformation using a robust autocorrelation estimator. Wir behandeln die robuste Schätzung eines linearen Trends bei autoregressiven Fehlern erster Ordnung. Die Repeated Median Regression zeigt ein gutes Verhalten bei positiven Korrelationen. Bei negativen Korrelationen ist eine Verbesserung durch eine Prais-Winsten Transformation mittels eines robusten Korrelationsschätzers möglich.

We discuss filtering procedures for robust extraction of a signal from noisy time series. Moving averages and running medians are standard methods for this, but they have shortcomings when large spikes (outliers) respectively trends occur. Modified trimmed means and linear median hybrid filters combine advantages of both approaches, but they do not completely overcome the difficulties. Improvements can be achieved by using robust regression methods, which work even in real time because of increased computational power and faster algorithms. Extending recent work we present filters for robust online signal extraction and discuss their merits for preserving trends, abrupt shifts and extremes and for the removal of spikes.

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.

We investigate the possibility of exploiting partial correlation graphs for identifying interpretable latent variables underlying a multivariate time series. It is shown how the collapsibility and separation properties of partial correlation graphs can be used to understand the relation between a factor model and the structure among the observable variables.

We examine the hypothesis of an increase of humus disintegration by analyzing chemical substances measured in the seepage water of a German forest. Problems arise because of a large percentage of missing observations. We use a regression model with spatial and temporal effects constructed in an exploratory data analysis. Spatial dependencies are modelled by random effects and an autoregressive structure for observations in distinct soil depths resulting in a recursive linear mixed model structure. Temporal dependencies are included by an autoregressive structure of the random effects. For parameter estimation an EM algorithm is deduced assuming the errors to be Gaussian. As a result of the data analysis we specify chemical substances which possibly affect the process of humus disintegration. In particular, we find evidence that the presence of aluminium ions is important, but because of the high correlations among the regressors this might be due to confounding with iron.

Data from the automatic monitoring of intensive care patients exhibits trends, outliers, and level changes as well as periods of relative constancy. All this is overlaid with a high level of noise and there are dependencies between the different items measured. Current monitoring systems tend to deliver too many false warnings which reduces their acceptability by medical staff. The challenge is to develop a method which allows a fast and reliable denoising of the data and which can separate artifacts from clinical relevant structural changes in the patients condition (Gather et al., 2002). A simple median filter works well as long as there is no substantial trend in the data but improvements may be possible by approximating the data by a local linear trend. As a first step in this programme the paper examines the relative merits of the L1 regression, the repeated median (Siegel, 1982) and the least median of squares (Hampel, 1975, Rousseeuw, 1984). The question of dependency between different items is a topic for future research.

Clinical information systems can record numerous variables describing the patient’s state at high sampling frequencies. Intelligent alarm systems and suitable bedside decision support are needed to cope with this flood of information. A basic task here is the fast and correct detection of important patterns of change such as level shifts and trends in the data. We present approaches for automated pattern detection in online-monitoring data. Several methods based on curve fitting and statistical time series analysis are described. Median filtering can be used as a preliminary step to reduce the noise and to remove clinically irrelevant short term fluctuations. Our special focus is the potential of these methods for online-monitoring in intensive care. The strengths and weaknesses of the methods are discussed in this special context. The best approach may well be a suitable combination of the methods for achieving reliable results. Further investigations are needed to further improve the methods and their performance should be compared extensively in simulation studies and applications to real data.

Methods of dimension reduction are very helpful and almost a necessity if we want to analyze high-dimensional time series since otherwise modelling affords many parameters because of interactions at various time-lags. We use a dynamic version of Sliced Inverse Regression (SIR; Li (1991)), which was developed to reduce the dimension of the regressor in regression problems, as an exploratory tool for analyzing multivariate time series. Analyzing each variable individually, we search for those directions, i.e., linear combinations of past and present observations of the other variables which explain most of the variability of the variable considered. This can also provide information on possible nonlinearities. We apply a dynamic version of SIR to multivariate physiological time series observed in intensive care.

In critical care extremely high dimensional time series are generated by clinical information systems. This yields new perspectives of data recording and also causes a new challenge for statistical methodology. Recently graphical correlation models have been developed for analysing the partial associations between the components of multivariate time series. We apply this technique to the hemodynamic system of critically ill patients monitored in intensive care. We appraise the practical value of the procedure by reidentifying known associations between the variables. From separate analyses for different pathophysiological states we conclude that distinct clinical states can be characterised by distinct partial correlation structures.

Intelligent alarm systems are needed for adequate bedside decision support in critical care. Clinical information systems acquire physiological variables online in short time intervals. To identify complications as well as therapeutic effects procedures for rapid classification of the current state of the patient have to be developed. Detection of characteristic patterns in the data can be accomplished by statistical time series analysis. In view of the high dimension of the data statistical methods for dimension reduction should be used in advance. We discuss the potential of statistical techniques for online monitoring.