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Ines Wilms

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Published work

18 published item(s)

preprint2026arXiv

FoReco and FoRecoML: A Unified Toolbox for Forecast Reconciliation in R

Forecast reconciliation has become key to improving the accuracy and coherence of forecasts for linearly constrained multiple time series, such as hierarchical and grouped series. Yet, comprehensive software that jointly covers cross-sectional, temporal, and cross-temporal reconciliation has so far been lacking. The R packages FoReco and FoRecoML address this gap by offering a comprehensive and unified framework. The packages respectively implement classical and regression-based linear reconciliation approaches, and non-linear approaches based on machine learning for cross-sectional, temporal and cross-temporal frameworks. Designed for accessibility and flexibility, these packages provide sensible default options that allow new users to apply reconciliation methods with minimal effort, while still giving expert users full control to explore state-of-the-art extensions through customized settings. With this dual focus, FoReco and FoRecoML are versatile tools for practitioners and researchers working on forecast reconciliation.

preprint2022arXiv

bootUR: An R Package for Bootstrap Unit Root Tests

Unit root tests form an essential part of any time series analysis. We provide practitioners with a single, unified framework for comprehensive and reliable unit root testing in the R package bootUR.The package's backbone is the popular augmented Dickey-Fuller test paired with a union of rejections principle, which can be performed directly on single time series or multiple (including panel) time series. Accurate inference is ensured through the use of bootstrap methods. The package addresses the needs of both novice users, by providing user-friendly and easy-to-implement functions with sensible default options, as well as expert users, by giving full user-control to adjust the tests to one's desired settings. Our parallelized C++ implementation ensures that all unit root tests are scalable to datasets containing many time series.

preprint2022arXiv

Detecting Anti-dumping Circumvention: A Network Approach

Despite the increasing integration of the global economic system, anti-dumping measures are a common tool used by governments to protect their national economy. In this paper, we propose a methodology to detect cases of anti-dumping circumvention through re-routing trade via a third country. Based on the observed full network of trade flows, we propose a measure to proxy the evasion of an anti-dumping duty for a subset of trade flows directed to the European Union, and look for possible cases of circumvention of an active anti-dumping duty. Using panel regression, we are able correctly classify 86% of the trade flows, on which an investigation of anti-dumping circumvention has been opened by the European authorities.

preprint2022arXiv

Hierarchical Regularizers for Mixed-Frequency Vector Autoregressions

Mixed-frequency Vector AutoRegressions (MF-VAR) model the dynamics between variables recorded at different frequencies. However, as the number of series and high-frequency observations per low-frequency period grow, MF-VARs suffer from the "curse of dimensionality". We curb this curse through a regularizer that permits hierarchical sparsity patterns by prioritizing the inclusion of coefficients according to the recency of the information they contain. Additionally, we investigate the presence of nowcasting relations by sparsely estimating the MF-VAR error covariance matrix. We study predictive Granger causality relations in a MF-VAR for the U.S. economy and construct a coincident indicator of GDP growth. Supplementary Materials for this article are available online.

preprint2022arXiv

Lasso Inference for High-Dimensional Time Series

In this paper we develop valid inference for high-dimensional time series. We extend the desparsified lasso to a time series setting under Near-Epoch Dependence (NED) assumptions allowing for non-Gaussian, serially correlated and heteroskedastic processes, where the number of regressors can possibly grow faster than the time dimension. We first derive an error bound under weak sparsity, which, coupled with the NED assumption, means this inequality can also be applied to the (inherently misspecified) nodewise regressions performed in the desparsified lasso. This allows us to establish the uniform asymptotic normality of the desparsified lasso under general conditions, including for inference on parameters of increasing dimensions. Additionally, we show consistency of a long-run variance estimator, thus providing a complete set of tools for performing inference in high-dimensional linear time series models. Finally, we perform a simulation exercise to demonstrate the small sample properties of the desparsified lasso in common time series settings.

preprint2022arXiv

Regularized Predictive Models for Beef Eating Quality of Individual Meals

Faced with changing markets and evolving consumer demands, beef industries are investing in grading systems to maximise value extraction throughout their entire supply chain. The Meat Standards Australia (MSA) system is a customer-oriented total quality management system that stands out internationally by predicting quality grades of specific muscles processed by a designated cooking method. The model currently underpinning the MSA system requires laborious effort to estimate and its prediction performance may be less accurate in the presence of unbalanced data sets where many "muscle x cook" combinations have few observations and/or few predictors of palatability are available. This paper proposes a novel predictive method for beef eating quality that bridges a spectrum of muscle x cook-specific models. At one extreme, each muscle x cook combination is modelled independently; at the other extreme a pooled predictive model is obtained across all muscle x cook combinations. Via a data-driven regularization method, we cover all muscle x cook-specific models along this spectrum. We demonstrate that the proposed predictive method attains considerable accuracy improvements relative to independent or pooled approaches on unique MSA data sets.

preprint2021arXiv

Tree-based Node Aggregation in Sparse Graphical Models

High-dimensional graphical models are often estimated using regularization that is aimed at reducing the number of edges in a network. In this work, we show how even simpler networks can be produced by aggregating the nodes of the graphical model. We develop a new convex regularized method, called the tree-aggregated graphical lasso or tag-lasso, that estimates graphical models that are both edge-sparse and node-aggregated. The aggregation is performed in a data-driven fashion by leveraging side information in the form of a tree that encodes node similarity and facilitates the interpretation of the resulting aggregated nodes. We provide an efficient implementation of the tag-lasso by using the locally adaptive alternating direction method of multipliers and illustrate our proposal's practical advantages in simulation and in applications in finance and biology.

preprint2020arXiv

High Dimensional Forecasting via Interpretable Vector Autoregression

Vector autoregression (VAR) is a fundamental tool for modeling multivariate time series. However, as the number of component series is increased, the VAR model becomes overparameterized. Several authors have addressed this issue by incorporating regularized approaches, such as the lasso in VAR estimation. Traditional approaches address overparameterization by selecting a low lag order, based on the assumption of short range dependence, assuming that a universal lag order applies to all components. Such an approach constrains the relationship between the components and impedes forecast performance. The lasso-based approaches work much better in high-dimensional situations but do not incorporate the notion of lag order selection. We propose a new class of hierarchical lag structures (HLag) that embed the notion of lag selection into a convex regularizer. The key modeling tool is a group lasso with nested groups which guarantees that the sparsity pattern of lag coefficients honors the VAR's ordered structure. The HLag framework offers three structures, which allow for varying levels of flexibility. A simulation study demonstrates improved performance in forecasting and lag order selection over previous approaches, and a macroeconomic application further highlights forecasting improvements as well as HLag's convenient, interpretable output.

preprint2016arXiv

Cellwise robust regularized discriminant analysis

Quadratic and Linear Discriminant Analysis (QDA/LDA) are the most often applied classification rules under normality. In QDA, a separate covariance matrix is estimated for each group. If there are more variables than observations in the groups, the usual estimates are singular and cannot be used anymore. Assuming homoscedasticity, as in LDA, reduces the number of parameters to estimate. This rather strong assumption is however rarely verified in practice. Regularized discriminant techniques that are computable in high-dimension and cover the path between the two extremes QDA and LDA have been proposed in the literature. However, these procedures rely on sample covariance matrices. As such, they become inappropriate in presence of cellwise outliers, a type of outliers that is very likely to occur in high-dimensional datasets. In this paper, we propose cellwise robust counterparts of these regularized discriminant techniques by inserting cellwise robust covariance matrices. Our methodology results in a family of discriminant methods that (i) are robust against outlying cells, (ii) cover the gap between LDA and QDA and (iii) are computable in high-dimension. The good performance of the new methods is illustrated through simulated and real data examples. As a by-product, visual tools are provided for the detection of outliers.

preprint2016arXiv

Commodity Dynamics: A Sparse Multi-class Approach

The correct understanding of commodity price dynamics can bring relevant improvements in terms of policy formulation both for developing and developed countries. Agricultural, metal and energy commodity prices might depend on each other: although we expect few important effects among the total number of possible ones, some price effects among different commodities might still be substantial. Moreover, the increasing integration of the world economy suggests that these effects should be comparable for different markets. This paper introduces a sparse estimator of the Multi-class Vector AutoRegressive model to detect common price effects between a large number of commodities, for different markets or investment portfolios. In a first application, we consider agricultural, metal and energy commodities for three different markets. We show a large prevalence of effects involving metal commodities in the Chinese and Indian markets, and the existence of asymmetric price effects. In a second application, we analyze commodity prices for five different investment portfolios, and highlight the existence of important effects from energy to agricultural commodities. The relevance of biofuels is hereby confirmed. Overall, we find stronger similarities in commodity price effects among portfolios than among markets.

preprint2016arXiv

Lasso-based forecast combinations for forecasting realized variances

Volatility forecasts are key inputs in financial analysis. While lasso based forecasts have shown to perform well in many applications, their use to obtain volatility forecasts has not yet received much attention in the literature. Lasso estimators produce parsimonious forecast models. Our forecast combination approach hedges against the risk of selecting a wrong degree of model parsimony. Apart from the standard lasso, we consider several lasso extensions that account for the dynamic nature of the forecast model. We apply forecast combined lasso estimators in a comprehensive forecasting exercise using realized variance time series of ten major international stock market indices. We find the lasso extended "ordered lasso" to give the most accurate realized variance forecasts. Multivariate forecast models, accounting for volatility spillovers between different stock markets, outperform univariate forecast models for longer forecast horizons.

preprint2016arXiv

Multi-class Vector AutoRegressive Models for Multi-store Sales Data

Retailers use the Vector AutoRegressive (VAR) model as a standard tool to estimate the effects of prices, promotions and sales in one product category on the sales of another product category. Besides, these price, promotion and sales data are available for not just one store, but a whole chain of stores. We propose to study cross-category effects using a multi-class VAR model: we jointly estimate cross-category effects for several distinct but related VAR models, one for each store. Our methodology encourages effects to be similar across stores, while still allowing for small differences between stores to account for store heterogeneity. Moreover, our estimator is sparse: unimportant effects are estimated as exactly zero, which facilitates the interpretation of the results. A simulation study shows that the proposed multi-class estimator improves estimation accuracy by borrowing strength across classes. Finally, we provide three visual tools showing (i) the clustering of stores on identical cross-category effects, (ii) the networks of product categories and (iii) the similarity matrices of shared cross-category effects across stores.

preprint2015arXiv

An algorithm for the multivariate group lasso with covariance estimation

We study a group lasso estimator for the multivariate linear regression model that accounts for correlated error terms. A block coordinate descent algorithm is used to compute this estimator. We perform a simulation study with categorical data and multivariate time series data, typical settings with a natural grouping among the predictor variables. Our simulation studies show the good performance of the proposed group lasso estimator compared to alternative estimators. We illustrate the method on a time series data set of gene expressions.

preprint2015arXiv

Identifying Demand Effects in a Large Network of Product Categories

Planning marketing mix strategies requires retailers to understand within- as well as cross-category demand effects. Most retailers carry products in a large variety of categories, leading to a high number of such demand effects to be estimated. At the same time, we do not expect cross-category effects between all categories. This paper outlines a methodology to estimate a parsimonious product category network without prior constraints on its structure. To do so, sparse estimation of the Vector AutoRegressive Market Response Model is presented. We find that cross-category effects go beyond substitutes and complements, and that categories have asymmetric roles in the product category network. Destination categories are most influential for other product categories, while convenience and occasional categories are most responsive. Routine categories are moderately influential and moderately responsive.

preprint2015arXiv

Robust Sparse Canonical Correlation Analysis

Canonical correlation analysis (CCA) is a multivariate statistical method which describes the associations between two sets of variables. The objective is to find linear combinations of the variables in each data set having maximal correlation. This paper discusses a method for Robust Sparse CCA. Sparse estimation produces canonical vectors with some of their elements estimated as exactly zero. As such, their interpretability is improved. We also robustify the method such that it can cope with outliers in the data. To estimate the canonical vectors, we convert the CCA problem into an alternating regression framework, and use the sparse Least Trimmed Squares estimator. We illustrate the good performance of the Robust Sparse CCA method in several simulation studies and two real data examples.

preprint2015arXiv

Sparse canonical correlation analysis from a predictive point of view

Canonical correlation analysis (CCA) describes the associations between two sets of variables by maximizing the correlation between linear combinations of the variables in each data set. However, in high-dimensional settings where the number of variables exceeds the sample size or when the variables are highly correlated, traditional CCA is no longer appropriate. This paper proposes a method for sparse CCA. Sparse estimation produces linear combinations of only a subset of variables from each data set, thereby increasing the interpretability of the canonical variates. We consider the CCA problem from a predictive point of view and recast it into a regression framework. By combining an alternating regression approach together with a lasso penalty, we induce sparsity in the canonical vectors. We compare the performance with other sparse CCA techniques in different simulation settings and illustrate its usefulness on a genomic data set.

preprint2015arXiv

Sparse cointegration

Cointegration analysis is used to estimate the long-run equilibrium relations between several time series. The coefficients of these long-run equilibrium relations are the cointegrating vectors. In this paper, we provide a sparse estimator of the cointegrating vectors. The estimation technique is sparse in the sense that some elements of the cointegrating vectors will be estimated as zero. For this purpose, we combine a penalized estimation procedure for vector autoregressive models with sparse reduced rank regression. The sparse cointegration procedure achieves a higher estimation accuracy than the traditional Johansen cointegration approach in settings where the true cointegrating vectors have a sparse structure, and/or when the sample size is low compared to the number of time series. We also discuss a criterion to determine the cointegration rank and we illustrate its good performance in several simulation settings. In a first empirical application we investigate whether the expectations hypothesis of the term structure of interest rates, implying sparse cointegrating vectors, holds in practice. In a second empirical application we show that forecast performance in high-dimensional systems can be improved by sparsely estimating the cointegration relations.

preprint2015arXiv

The predictive power of the business and bank sentiment of firms: A high-dimensional Granger Causality approach

We study the predictive power of industry-specific economic sentiment indicators for future macro-economic developments. In addition to the sentiment of firms towards their own business situation, we study their sentiment with respect to the banking sector - their main credit providers. The use of industry-specific sentiment indicators results in a high-dimensional forecasting problem. To identify the most predictive industries, we present a bootstrap Granger Causality test based on the Adaptive Lasso. This test is more powerful than the standard Wald test in such high-dimensional settings. Forecast accuracy is improved by using only the most predictive industries rather than all industries.