Two Procedures for Robust Monitoring of Probability Distributions of Economic Data Streams induced by Depth Functions

Data streams (streaming data) consist of transiently observed, evolving in time, multidimensional data sequences that challenge our computational and/or inferential capabilities. In this paper we propose user friendly approaches for robust monitoring of selected properties of unconditional and conditional distribution of the stream basing on depth functions. Our proposals are robust to a small fraction of outliers and/or inliers but sensitive to a regime change of the stream at the same time. Their implementations are available in our free R package DepthProc.Comment: Operations Research and Decisions, vol. 25, No. 1, 201

Poisson regression charts for the monitoring of surveillance time series

This paper presents a Poisson control chart for monitoring time series of counts typically arising in the surveillance of infectious diseases. The in-control mean is assumed to be time-varying and linear on the log-scale with intercept and seasonal components. If a shift in the intercept occurs the system goes out-of-control. Novel is that the magnitude of the shift does not have to be specified in advance: using the generalized likelihood ratio (GLR) statistic a monitoring scheme is formulated to detect on-line whether a shift in the intercept occurred. For this specific Poisson chart the necessary quantities of the GLR detector can be efficiently computed by recursive formulas. Extensions to more general Poisson charts e.g. containing an autoregressive epidemic component are discussed. Using Monte Carlo simulations run length properties of the proposed schemes are investigated. The practicability of the charts is demonstrated by applying them to the observed number of salmonella hadar cases in Germany 2001-2006

Effects of Applying Linear and Nonlinear Filters on Tests for Unit Roots with Additive Outliers

Conventional univariate Dickey-Fuller tests tend to produce spurious stationarity when there exist additive outlying observations in the time series. Correct critical values are usually obtained by adding dummy variables to the Dickey-Fuller regression. This is a nice theoretical result but not attractive from the empirical point of view since almost any result can be obtained just by a convenient selection of dummy variables. In this paper we suggest a robust procedure based on running Dickey-Fuller tests on the trend component instead of the original series. We provide both finite-sample and large-sample justifications. Practical implementation is illustrated through an empirical example based on the US/Finland real exchange rate series.Additive outliers, Dickey-Fuller test, Linear and nonlinear filtering, Bootstrap

Modified repeated median filters

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. --signal extraction,robust filtering,drifts,jumps,outliers,computational geometry,update algorithm

Robust Kalman tracking and smoothing with propagating and non-propagating outliers

A common situation in filtering where classical Kalman filtering does not perform particularly well is tracking in the presence of propagating outliers. This calls for robustness understood in a distributional sense, i.e.; we enlarge the distribution assumptions made in the ideal model by suitable neighborhoods. Based on optimality results for distributional-robust Kalman filtering from Ruckdeschel[01,10], we propose new robust recursive filters and smoothers designed for this purpose as well as specialized versions for non-propagating outliers. We apply these procedures in the context of a GPS problem arising in the car industry. To better understand these filters, we study their behavior at stylized outlier patterns (for which they are not designed) and compare them to other approaches for the tracking problem. Finally, in a simulation study we discuss efficiency of our procedures in comparison to competitors.Comment: 27 pages, 12 figures, 2 table

Probing the dynamics of identified neurons with a data-driven modeling approach

In controlling animal behavior the nervous system has to perform within the operational limits set by the requirements of each specific behavior. The implications for the corresponding range of suitable network, single neuron, and ion channel properties have remained elusive. In this article we approach the question of how well-constrained properties of neuronal systems may be on the neuronal level. We used large data sets of the activity of isolated invertebrate identified cells and built an accurate conductance-based model for this cell type using customized automated parameter estimation techniques. By direct inspection of the data we found that the variability of the neurons is larger when they are isolated from the circuit than when in the intact system. Furthermore, the responses of the neurons to perturbations appear to be more consistent than their autonomous behavior under stationary conditions. In the developed model, the constraints on different parameters that enforce appropriate model dynamics vary widely from some very tightly controlled parameters to others that are almost arbitrary. The model also allows predictions for the effect of blocking selected ionic currents and to prove that the origin of irregular dynamics in the neuron model is proper chaoticity and that this chaoticity is typical in an appropriate sense. Our results indicate that data driven models are useful tools for the in-depth analysis of neuronal dynamics. The better consistency of responses to perturbations, in the real neurons as well as in the model, suggests a paradigm shift away from measuring autonomous dynamics alone towards protocols of controlled perturbations. Our predictions for the impact of channel blockers on the neuronal dynamics and the proof of chaoticity underscore the wide scope of our approach