Research

Abstract: We study a simple ℓ1-regularized generalized least-squares (GLS) estimator for high-dimensional regressions with autocorrelated errors. The estimation procedure consists of three steps: performing a LASSO regression, fitting an autoregressive model to the realized residuals, and then running a second-stage LASSO regression on the rotated (whitened) data. We examine the theoretical performance of the method in a sub-Gaussian random-design setting, in particular assessing the impact of the rotation on the design matrix and how this impacts the estimation error of the procedure. We show that the GLS (and a feasible variant) maintains a smaller estimation error than an unadjusted LASSO regression when the errors are driven by an autoregressive process. A simulation study verifies the performance of the proposed method, demonstrating that the penalized (feasible) GLS-LASSO estimator performs on par with the LASSO in the case of white noise errors, whilst outperforming when the errors exhibit significant autocorrelation. .

Abstract: Low-frequency time-series (e.g., quarterly data) are often treated as benchmarks for interpolating to higher frequencies, since they generally exhibit greater precision and accuracy in contrast to their high-frequency counterparts (e.g., monthly data) reported by governmental bodies. An array of regression-based methods have been proposed in the literature which aim to estimate a target high-frequency series using higher frequency indicators. However, in the era of big data and with the prevalence of large volume of administrative data-sources there is a need to extend traditional methods to work in high-dimensional settings, i.e. where the number of indicators is similar or larger than the number of low-frequency samples. The package DisaggregateTS includes both classical regressionsbased disaggregation methods alongside recent extensions to high-dimensional settings, c.f. Mosley et al. (2022). This paper provides guidance on how to implement these methods via the package in R, and demonstrates their use in an application to disaggregating CO2 emissions. 

Keywords: GHG emissions, temperature target, carbon markets, emission abatement, stochastic radiative forcing; 

Abstract: We study optimal climate risk mitigation with short-term emissions-reduction targets and long-run temperature stabilization goals in the presence of firms that generate greenhouse gases with different atmospheric persistence and warming potential. We investigate how the pervasive notion of carbon equivalence may undermine climate risk mitigation when carbon markets allow short-lived gases to be traded against long-lived ones. Our findings demonstrate the vulnerability of certain emissions metrics and carbon-accounting standards to greenwashing, and support reporting emissions in disaggregated form and in gas-specific mass units. 

Keywords: GHG emissions, temperature target, carbon markets, emission abatement, stochastic radiative forcing; 

Abstract: Manski's nonparametric bounds partially identify the average treatment effects (ATEs) under minimal assumptions, yielding an interval-valued estimand with endpoints that depend on the outcome support - typically treated as known or fixed. In many empirical settings, however, credible bounds on the outcome support are often unavailable and outcomes may be heavy-tailed, so common empirical implementations that rely on ad-hoc truncation or observed extrema can compromise finite-sample coverage. We develop concATE, a hybrid confidence band for interval-identified ATEs that explicitly accounts for tail uncertainty without imposing parametric assumptions. The inference method combines a distribution-free concentration bound for the outcome distribution based on the Dvoretzky-Kiefer-Wolfowitz inequality with the asymptotic delta-method inference for smooth mean components, and allocates size across bound endpoints using Bonferroni's inequality to guarantee joint coverage. We further extend concATE to a group-sequential procedure that controls the family-wise error rate using Pocock correction. Applying the method to panel data on 901 listed firms (2015Q2--2022Q1), we find that senior-level gender diversity has a statistically significant positive effect on firm value (Tobin's Q) only after crossing substantial representation thresholds: in Growth & Innovation sectors, significance emerges at approximately 55% female leadership, while in Defensive sectors it appears only beyond about 60%. 

Keywords: Stochastic regressors; persistency; sign test; point-optimal test; nonlinear model; heteroskedasticity; exact inference; distribution-free; split-sample; adaptive method; projection technique; numerical optimization.

Abstract: We propose point-optimal sign-based tests for linear and nonlinear predictive regressions that are valid in the presence of heteroskedasticity of unknown form and persistent volatility, as well as persistent regressors and heavy-tailed errors. These tests are exact, distribution-free, and may be inverted to build confidence regions for the parameters of the regression function. Point-optimal tests maximize power at a predetermined point in the alternative hypothesis parameter space, which in practice is unknown. Therefore, we suggest an adaptive approach based on the split-sample technique to shift the power function close to that of the power envelope. We then present a Monte Carlo study to assess the performance of the proposed “quasi”-point-optimal sign test by comparing its size and power to those of certain existing tests which are intended to be robust against heteroskedasticity. The results show that our procedures outperform classical tests. Finally, as predictors of stock returns are often highly persistent and lead to invalid inference using conventional tests, we consider an empirical application to illustrate the relevance of our proposed tests for testing the predictability of stock returns.

Keywords: D-vine; persistency; sign test; point-optimal test; exact inference; distribution-free; split-sample; power envelope; 

Abstract: We propose pair copula constructed point-optimal sign tests in the context of linear and nonlinear predictive regressions with endogenous, persistent regressors, and disturbances exhibiting serial (nonlinear) dependence. The proposed approaches entail considering the entire dependence structure of the signs and building feasible test statistics based on pair copula constructions of the sign process. The tests are exact and valid in the presence of heavy tailed and nonstandard errors, as well as heterogeneous and persistent volatility. Furthermore, they may be inverted to build confidence regions for the parameters of the regression function. Finally, we adopt an adaptive approach based on the split-sample technique to Maximize the power of the test. In a Monte Carlo study, we compare the performance of the proposed  "quasi"-point-optimal sign tests based on pair copula constructions by comparing its size and power to those of certain existing tests that are intended to be robust against heteroskedasticity. The simulation results maintain the superiority of our procedures to existing popular tests.

Keywords: 

Abstract: Offline sparse regression and its generalized counterpart, whereby the errors are assumed to exhibit linear dependence have been studied extensively, both asymptotically and non-asymptotically. With the advent of high-frequency data and algorithms, recent literature has diverted attention to online sparse estimation of these models, where an initial batch is used to compute a starting estimator, and the support and regularization parameters are subsequently updated as new data arrive. In this paper, we propose efficient GLS and FGLS extensions of these algorithms in the presence of autocorrelated errors and derive their non-asymptotic properties. Numerical experiments show the efficiency and superiority of this approach to online LASSO in the presence of autocorrelated errors.

Keywords: 

Abstract: We consider the projection of sovereign ratings along selected NGFS climate scenarios for a large panel of countries to quantify the impact of climate risk on sovereign bond portfolios. We first identify macro variables driving probabilities of default (PDs) and then project such variables along relevant climate pathways by using an econometric approach and an equilibrium model. We generate term structures of PDs and ratings along each climate scenario, by allowing for both transition and physical climatic risks. The results are used to quantify the impact of climate risk scenarios on sovereign bond portfolios and to document the importance of counterfactuals in designing and implementing climate stress tests. 

Keywords: Causality measures; time series; Kullback-Leibler distance; bootstrap; Bonferroni test.

Abstract: We propose sign-based measures of Granger causality based on the Kullback-Leibler distance that quantify the degree of causalities. Furthermore, we show that by using bound-type procedures, Granger non-causality tests between random variables can be developed as a byproduct of the sign-based measures. The tests are exact, distribution-free and robust against heteroskedasticity of unknown form. Additionally, as in the first chapter, we impose a Markovian assumption on the sign process to obtain feasible measures and tests of causality. To estimate the sign-based measures, we suggest the use of vector autoregressive sieve bootstrap to reduce the bias and obtain bias-corrected estimators. Furthermore, we discuss the validity of the bootstrap technique. A Monte Carlo simulation study reveals that the bootstrap bias-corrected estimator of the causality measures produce the desired outcome. Furthermore, the tests of Granger non-causality based on the signs perform well in terms of size control and power. Finally, an empirical application is considered to illustrate the practical relevance of the sign-based causality measures and tests.