Robust online signal extraction from multivariate time series

We introduce robust regression-based online filters for multivariate time series and discuss their performance in real time signal extraction settings. We focus on methods that can deal with time series exhibiting patterns such as trends, level changes, outliers and a high level of noise as well as periods of a rather steady state. In particular, the data may be measured on a discrete scale which often occurs in practice. Our new filter is based on a robust two-step online procedure. We investigate its relevant properties and its performance by means of simulations and a medical application. --Multivariate time series,signal extraction,robust regression,online methods

Robust misspecification tests for the Heckman’s two-step estimator

We construct and evaluate LM and Neyman’s C(α) tests based on bivariate Edgeworth expansions for the consistency of the Heckman’s two-step estimator in selection models, that is, for the marginal normality and linearity of the conditional expectation of the error terms. The proposed tests are robust to local misspecification in nuisance distributional parameters. Monte Carlo results show that instead of testing bivariate normality, testing marginal normality and linearity of the conditional expectations separately have a better size performance. Moreover, the robust variants of the tests have better size and similar power to non-robust tests, which determines that these tests can be successfully applied to detect specific departures from the null model of bivariate normality. We apply the tests procedures to women’s labor supply data

A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations

We extend the important idea of range-based volatility estimation to the multivariate case. In particular, we propose a range-based covariance estimator that is motivated by financial economic considerations (the absence of arbitrage), in addition to statistical considerations. We show that, unlike other univariate and multivariate volatility estimators, the range-based estimator is highly efficient yet robust to market microstructure noise arising from bid-ask bounce and asynchronous trading. Finally, we provide an empirical example illustrating the value of the high-frequency sample path information contained in the range-based estimates in a multivariate GARCH framework.Range-based estimation, volatility, covariance, correlation, absence of arbitrage, exchange rates, stock returns, bond returns, bid-ask bounce, asynchronous trading

Multiariate Wavelet-based sahpe preserving estimation for dependant observation

We present a new approach on shape preserving estimation of probability distribution and density functions using wavelet methodology for multivariate dependent data. Our estimators preserve shape constraints such as monotonicity, positivity and integration to one, and allow for low spatial regularity of the underlying functions. As important application, we discuss conditional quantile estimation for financial time series data. We show that our methodology can be easily implemented with B-splines, and performs well in a finite sample situation, through Monte Carlo simulations.Conditional quantile; time series; shape preserving wavelet estimation; B-splines; multivariate process

On detecting jumps in time series: Nonparametric setting

Motivated by applications in statistical quality control and signal analysis, we propose a sequential detection procedure which is designed to detect structural changes, in particular jumps, immediately. This is achieved by modifying a median filter by appropriate kernel-based jump preserving weights (shrinking) and a clipping mechanism. We aim at both robustness and immediate detection of jumps. Whereas the median approach ensures robust smooths when there are no jumps, the modification ensure immediate reaction to jumps. For general clipping location estimators we show that the procedure can detect jumps of certain heights with no delay, even when applied to Banach space valued data. For shrinking medians we provide an asymptotic upper bound for the normed delay. The finite sample properties are studied by simulations which show that our proposal outperforms classical procedures in certain respects. --Edge Detection,Nonparametric Estimation,Quality Control,Statistical Process Control

Robust Learning from Bites for Data Mining

Some methods from statistical machine learning and from robust statistics have two drawbacks. Firstly, they are computer-intensive such that they can hardly be used for massive data sets, say with millions of data points. Secondly, robust and non-parametric confidence intervals for the predictions according to the fitted models are often unknown. Here, we propose a simple but general method to overcome these problems in the context of huge data sets. The method is scalable to the memory of the computer, can be distributed on several processors if available, and can help to reduce the computation time substantially. Our main focus is on robust general support vector machines (SVM) based on minimizing regularized risks. The method offers distribution-free confidence intervals for the median of the predictions. The approach can also be helpful to fit robust estimators in parametric models for huge data sets. --Breakdown point,convex risk minimization,data mining,distributed computing,influence function,logistic regression,robustness,scalability

Wake me up before you GO-GARCH

In this paper we present a new three-step approach to the estimation of Generalized Orthogonal GARCH (GO-GARCH) models, as proposed by van der Weide (2002). The approach only requires (non-linear) least-squares methods in combination with univariate GARCH estimation, and as such is computationally attractive, especially in largerdimensional systems, where a full likelihood optimization is often infeasible. The eï¬~@ectiveness of the method is investigated using Monte Carlo simulations as well as a number of empirical applications.

Fast robust correlation for high-dimensional data

The product moment covariance is a cornerstone of multivariate data analysis, from which one can derive correlations, principal components, Mahalanobis distances and many other results. Unfortunately the product moment covariance and the corresponding Pearson correlation are very susceptible to outliers (anomalies) in the data. Several robust measures of covariance have been developed, but few are suitable for the ultrahigh dimensional data that are becoming more prevalent nowadays. For that one needs methods whose computation scales well with the dimension, are guaranteed to yield a positive semidefinite covariance matrix, and are sufficiently robust to outliers as well as sufficiently accurate in the statistical sense of low variability. We construct such methods using data transformations. The resulting approach is simple, fast and widely applicable. We study its robustness by deriving influence functions and breakdown values, and computing the mean squared error on contaminated data. Using these results we select a method that performs well overall. This also allows us to construct a faster version of the DetectDeviatingCells method (Rousseeuw and Van den Bossche, 2018) to detect cellwise outliers, that can deal with much higher dimensions. The approach is illustrated on genomic data with 12,000 variables and color video data with 920,000 dimensions