Sarah Gelper

Sparse least trimmed squares regression for analyzing high-dimensional large data sets

Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the data. This paper combines robust regression and sparse model estimation. A robust and sparse estimator is introduced by adding an L1penalty on the coefficient estimates to the well-known least trimmed squares (LTS) estimator. The breakdown point of this sparse LTS estimator is derived, and a fast algorithm for its computation is proposed. In addition, the sparse LTS is applied to protein and gene expression data of the NCI-60 cancer cell panel. Both a simulation study and the real data application show that the sparse LTS has better prediction performance than its competitors in the presence of leverage points.

Consumer Sentiment and Consumer Spending: Decomposing the Granger Causal Relationship in the Time Domain

It is often believed that the consumer sentiment index has predictive power for future consumption levels. While Granger causality tests have already been used to test for this, no attempt has been made yet to quantify the predictive power of the consumer sentiment index over different time horizons. In this article, we decompose the Granger causality at different time lags, by looking at a sequence of nested prediction models. Since the consumer sentiment index turns out to be cointegrated with real consumption, we resort to error correcting models. Four consumption series are studied, namely total real consumption, real consumption of durables, non-durables and services. Among other findings, we show that the consumer sentiment index Granger causes future consumption with an average time lag of 4–5 months. Furthermore, it is found that the consumer sentiment index has more incremental predictive power for consumption of services than for consumption of durables or non-durables, and that the index is not only useful as a predictor at the very short term, but keeps predictive power at larger time horizons.

Multivariate out-of-sample tests for Granger causality

A time series is said to Granger cause another series if it has incremental predictive power when forecasting it. While Granger causality tests have been studied extensively in the univariate setting, much less is known for the multivariate case. Multivariate out-of-sample tests for Granger causality are proposed and their performance is measured by a simulation study. The results are graphically represented by size-power plots. It emerges that the multivariate regression test is the most powerful among the considered possibilities. As a real data application, it is investigated whether the consumer confidence index Granger causes retail sales in Germany, France, the Netherlands and Belgium.

On the construction of the European economic sentiment indicator

Economic sentiment surveys are carried out by all European Union member states and are often seen as early indicators for future economic developments. Based on these surveys, the European Commission constructs an aggregate European Economic Sentiment Indicator (ESI). This paper compares the ESI with more sophisticated aggregation schemes based on statistical methods: dynamic factor analysis and partial least squares. The indicator based on partial least squares clearly outperforms the other two indicators in terms of comovement with economic activity. In terms of forecast ability, the ESI, constructed in a rather ad hoc way, can compete with the other indicators.

Robust exponential smoothing of multivariate time series

Multivariate time series may contain outliers of different types. In the presence of such outliers, applying standard multivariate time series techniques becomes unreliable. A robust version of multivariate exponential smoothing is proposed. The method is affine equivariant, and involves the selection of a smoothing parameter matrix by minimizing a robust loss function. It is shown that the robust method results in much better forecasts than the classic approach in the presence of outliers, and performs similarly when the data contain no outliers. Moreover, the robust procedure yields an estimator of the smoothing parameter less subject to downward bias. As a byproduct, a cleaned version of the time series is obtained, as is illustrated by means of a real data example.

The Predictive Power of the European Economic Sentiment Indicator

Economic sentiment surveys are carried out by all European Union member states on a monthly basis. The survey outcomes are used to obtain early insight into future economic evolutions and often receive extensive press coverage. Based on these surveys, the European Commission constructs an aggregate European Economic Sentiment Indicator (ESI). This paper compares the ESI with more sophisticated aggregation schemes based on two statistical methods: dynamic factor analysis and partial least squares. We compare the aggregate sentiment indicators and the weights used in their construction. Afterwards a comparison of their forecast performance for two real economic series, industrial production growth and unemployment, follows. Our findings are twofold. First it is found that the ESI, although constructed in a rather ad hoc way, can compete with the indicators constructed according to statistical principles. Secondly, the predictive power of the sentiment indicators, as tested for in an out-of sample Granger causality framework, is limited.

Robust control charts for time series data

This article presents a control chart for time series data, based on the one-step- ahead forecast errors of the Holt-Winters forecasting method. We use robust techniques to prevent that outliers affect the estimation of the control limits of the chart. Moreover, robustness is important to maintain the reliability of the control chart after the occurrence of alarm observations. The properties of the new control chart are examined in a simulation study and on a real data example.

Robust groupwise least angle regression

Many regression problems exhibit a natural grouping among predictor variables. Examples are groups of dummy variables representing categorical variables, or present and lagged values of time series data. Since model selection in such cases typically aims for selecting groups of variables rather than individual covariates, an extension of the popular least angle regression (LARS) procedure to groupwise variable selection is considered. Data sets occurring in applied statistics frequently contain outliers that do not follow the model or the majority of the data. Therefore a modification of the groupwise LARS algorithm is introduced that reduces the influence of outlying data points. Simulation studies and a real data example demonstrate the excellent performance of groupwise LARS and, when outliers are present, its robustification.

Sparse Least Trimmed Squares Regression

Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the data. This paper combines robust regression and sparse model estimation. A robust and sparse estimator is introduced by adding an L1 penalty on the coefficient estimates to the well known least trimmed squares (LTS) estimator. The breakdown point of this sparse LTS estimator is derived, and a fast algorithm for its computation is proposed. Both the simulation study and the real data example show that the LTS has better pre- diction performance than its competitors in the presence of leverage points.

Robust Online Scale Estimation in Time Series: A Regression-Free Approach

This paper presents variance extraction procedures for univariate time series. The volatility of a times series is monitored allowing for non-linearities, jumps and outliers in the level. The volatility is measured using the height of triangles formed by consecutive observations of the time series. This idea was proposed by Rousseeuw and Hubert (1996, Regression-free and robust estimation of scale for bivariate data, Computational Statistics and Data Analysis, 21, 67{85) in the bivariate setting. This paper extends their procedure to apply for online scale estimation in time series analysis. The statistical properties of the new methods are derived and nite sample properties are given. A nancial and a medical application illustrate the use of the procedures.