Research Projects
This page provides more information on the research projects carried out in the context of my Marie Curie action BigTime.
Structured Regularizers for High-dimensional Time Series Models
Large time series data sets nowadays pervade every domain of science, business and economics. We develop a new class of convex regularizers for large dynamic systems.
Vector AutoRegressions (VARs) form a fundamental tool for modeling multivariate time series. Yet, they easily suffer from the curse of dimensionality since the number of parameters increases quadratically with the number of component series, as graphically visualized below.
In Nicholson et al. (2021), we propose hierarchical lag structures, called “HLag”, that simultaneously perform dimension reduction through sparsity and incorporate the notion of lag order selection into a convex regularizer. Through macroeconomic, financial, and energy applications, we highlight Hlag’s forecasting improvements as well as its convenient, interpretable output.
Next, we extend the methodology to Vector AutoRegressive Moving Average (VARMA) models. In practice, identifiability issues have led many authors to abandon VARMA models in favor of the simpler VAR. Such a practice is unfortunate since even very simple VARMAs can have quite complicated VAR representations. In Wilms et al. (2019), we narrow this gap with a new optimization-based approach to VARMA identification that is built upon the principle of parsimony.
While VARs and VARMAs are cornerstones in multivariate time series analysis; they typically require all component series to enter the model at the same frequency. In practice, however, macro and financial series are typically recorded at different frequencies; quarterly, monthly, weekly or daily for instance. In Hecq et al. (2021), we therefore extend the HLag methodology to a Mixed-Frequency VAR framework.
The HLag estimator for VARs and VARMA are available in the R package bigtime, the package hierarchical-MFVAR tackles mixed-frequency models.
Network Analysis of Large Dynamic Systems
In this research line, we focus on network models of large time series systems to describe how multivariate time series interact. We consider several economic applications.
In Barbaglia et al. (2020), we consider a network of commodities and study volatility spillovers (i.e. lagged effects) among a large number of energy, biofuel and agricultural commodities. In Wilms et al. (2021), we study realized variances of several major international stock market indices and use network analysis to study the time varying nature of volatility spillovers. In Hecq et al. (2021), we study predictive Granger causality relations in a MF-VAR for the US economy and construct a coincident indicator of GDP growth.
Inference for High-dimensional Time Series Models
Next to accurate estimation in high-dimensional time series settings, reliable uncertainty quantification is also key. We provide penalized regression methods for honest uncertainty quantification in high-dimensional time series models. In Smeekes and Wilms (2020), we focus on unit root tests. Unit root tests form an essential part of any time series analysis. We use bootstrap methods to provide accurate and reliable inference in practice. The software package bootUR provides practitioners with a single, unified framework for comprehensive and reliable unit root testing on single time series or potentially large systems of time series (including panels).
In Adamek et al. (2020), we develop honest methods for inference in large time series models. Building on the desparsified lasso, we develop uniformly valid inference for high-dimensional time series models that explicitly accounts for model uncertainty and remains valid under general conditions that characterize many econometric applications. You can explore the methodology through the R package desla.
