arXiv subjects

Alain Hecq

Publications and source records attributed to Alain Hecq.

At least 19 recordsLinked to original sources

arXiv2026

Nonfundamentalness or missing information ? Evidence from causal-noncausal VARs in macro-finance

This paper studies the presence of noncausal dynamics in standard macro-finance VAR models and asks whether they reflect genuine nonfundamentalness or omitted information available to economic agents but unobserved by the econometrician. To that end, we introduce a factor-filtering mixed causal-noncausal VARX approach designed to account for common macroeconomic information. We assess its performance in simulated settings, while showing also that the generalized covariance (GCov) estimator correctly recovers causal and noncausal dynamics when using several lags. Empirically, we revisit the well-known Stock-Watson monetary policy (S)VAR and show that the noncausal components detected in the baseline specification largely disappear once common factors are filtered out. Finally, we compare impulse responses from the filtered and original data to assess the transmission of monetary policy shocks and show that filtering further removes the price puzzle.

econ.EM↗

arXiv2026

Seasonality in Mixed Causal-Noncausal Processes

This paper investigates the role of complex and negative roots in mixed causal-noncausal autoregressive (MAR) models. Using partial fraction decompositions, we show that seasonal roots can always be isolated in the moving average representation of purely causal and noncausal AR models. We find that this result extends to the MAR model, which means that no new joint seasonal effects can be generated despite the multiplicative structure of the causal and noncausal polynomials. This results has important consequences for the MAR model selection procedure and these are extensively studied in a Monte Carlo simulation study. An empirical application on COVID-19 and soybean data illustrates the main findings of the paper.

econ.EM↗

arXiv2026

Shrinkage Regularization for (Non)Linear Serial Dependence Test

This paper introduces a regularized test of the null hypothesis of the absence of linear and nonlinear serial dependence for high-dimensional non-Gaussian time series. Our approach extends the portmanteau test introduced in Jasiak and Neyazi (2023) to the high-dimensional setting.

econ.EM↗

arXiv2025

Decomposing Co-Movements in Matrix-Valued Time Series: A Pseudo-Structural Reduced-Rank Approach

A pseudo-structural framework is proposed for analyzing contemporaneous co-movements in stationary reduced-rank matrix autoregressive (RRMAR) models. Unlike conventional vector autoregressive (VAR) models that discard the matrix structure, the formulation preserves it, enabling a decomposition of co-movements into three interpretable components: row-specific, column-specific, and joint (row--column) interactions across the matrix-valued time series. The estimator admits standard asymptotic inference and a BIC-type criterion is proposed for the joint selection of the reduced ranks and the autoregressive lag order. The method's finite-sample performance in terms of estimation accuracy, coverage, and rank selection is validated through simulation experiments, including cases of rank misspecification. Practical usefulness is illustrated through an application to labor market data from nine Midwestern U.S. states, revealing distinct row-, column-, and joint co-movement patterns.

econ.EM↗

arXiv2025

Bubble Detection with Application to Green Bubbles: A Noncausal Approach

This paper introduces a new approach for bubble detection based on mixed causal and noncausal autoregressive processes and their tail process representation during an explosive episode. Departing from traditional definitions of bubbles as nonstationary and temporarily explosive processes, we adopt a perspective in which prices are assumed to follow a strictly stationary process, with the bubble considered an intrinsic component of its nonlinear dynamics. The proposed approach provides a bubble indicator for detecting bubbles and measuring their duration. We implement our strategy to investigate the phenomenon called the "green bubble" in the field of renewable energy investment.

econ.EM↗

arXiv2025

Regularized Generalized Covariance (RGCov) Estimator

We introduce a regularized Generalized Covariance (RGCov) estimator as an extension of the GCov estimator to high dimensional setting that results either from high-dimensional data or a large number of nonlinear transformations used in the objective function. The approach relies on a ridge-type regularization for high-dimensional matrix inversion in the objective function of the GCov. The RGCov estimator is consistent and asymptotically normally distributed. We provide the conditions under which it can reach semiparametric efficiency and discuss the selection of the optimal regularization parameter. We also examine the diagonal GCov estimator, which simplifies the computation of the objective function. The GCov-based specification test, and the test for nonlinear serial dependence (NLSD) are extended to the regularized RGCov specification and RNLSD tests with asymptotic Chi-square distributions. Simulation studies show that the RGCov estimator and the regularized tests perform well in the high dimensional setting. We apply the RGCov to estimate the mixed causal and noncausal VAR model of stock prices of green energy companies.

econ.EM↗

arXiv2024

Detecting Cointegrating Relations in Non-stationary Matrix-Valued Time Series

This paper proposes a Matrix Error Correction Model to identify cointegration relations in matrix-valued time series. We hereby allow separate cointegrating relations along the rows and columns of the matrix-valued time series and use information criteria to select the cointegration ranks. Through Monte Carlo simulations and a macroeconomic application, we demonstrate that our approach provides a reliable estimation of the number of cointegrating relationships.

econ.EM↗

arXiv2024

Reduced-Rank Matrix Autoregressive Models: A Medium $N$ Approach

Reduced-rank regressions are powerful tools used to identify co-movements within economic time series. However, this task becomes challenging when we observe matrix-valued time series, where each dimension may have a different co-movement structure. We propose reduced-rank regressions with a tensor structure for the coefficient matrix to provide new insights into co-movements within and between the dimensions of matrix-valued time series. Moreover, we relate the co-movement structures to two commonly used reduced-rank models, namely the serial correlation common feature and the index model. Two empirical applications involving U.S.\ states and economic indicators for the Eurozone and North American countries illustrate how our new tools identify co-movements.

econ.EM↗

arXiv2023

Spectral identification and estimation of mixed causal-noncausal invertible-noninvertible models

This paper introduces new techniques for estimating, identifying and simulating mixed causal-noncausal invertible-noninvertible models. We propose a framework that integrates high-order cumulants, merging both the spectrum and bispectrum into a single estimation function. The model that most adequately represents the data under the assumption that the error term is i.i.d. is selected. Our Monte Carlo study reveals unbiased parameter estimates and a high frequency with which correct models are identified. We illustrate our strategy through an empirical analysis of returns from 24 Fama-French emerging market stock portfolios. The findings suggest that each portfolio displays noncausal dynamics, producing white noise residuals devoid of conditional heteroscedastic effects.

econ.EM↗

arXiv2023

Optimization of the Generalized Covariance Estimator in Noncausal Processes

This paper investigates the performance of the Generalized Covariance estimator (GCov) in estimating and identifying mixed causal and noncausal models. The GCov estimator is a semi-parametric method that minimizes an objective function without making any assumptions about the error distribution and is based on nonlinear autocovariances to identify the causal and noncausal orders. When the number and type of nonlinear autocovariances included in the objective function of a GCov estimator is insufficient/inadequate, or the error density is too close to the Gaussian, identification issues can arise. These issues result in local minima in the objective function, which correspond to parameter values associated with incorrect causal and noncausal orders. Then, depending on the starting point and the optimization algorithm employed, the algorithm can converge to a local minimum. The paper proposes the use of the Simulated Annealing (SA) optimization algorithm as an alternative to conventional numerical optimization methods. The results demonstrate that SA performs well when applied to mixed causal and noncausal models, successfully eliminating the effects of local minima. The proposed approach is illustrated by an empirical application involving a bivariate commodity price series.

econ.EM↗

arXiv2023

Inference in Non-stationary High-Dimensional VARs

In this paper we construct an inferential procedure for Granger causality in high-dimensional non-stationary vector autoregressive (VAR) models. Our method does not require knowledge of the order of integration of the time series under consideration. We augment the VAR with at least as many lags as the suspected maximum order of integration, an approach which has been proven to be robust against the presence of unit roots in low dimensions. We prove that we can restrict the augmentation to only the variables of interest for the testing, thereby making the approach suitable for high dimensions. We combine this lag augmentation with a post-double-selection procedure in which a set of initial penalized regressions is performed to select the relevant variables for both the Granger causing and caused variables. We then establish uniform asymptotic normality of a second-stage regression involving only the selected variables. Finite sample simulations show good performance, an application to investigate the (predictive) causes and effects of economic uncertainty illustrates the need to allow for unknown orders of integration.

econ.EM↗

arXiv2023

Hierarchical Regularizers for Reverse Unrestricted Mixed Data Sampling Regressions

Reverse Unrestricted MIxed DAta Sampling (RU-MIDAS) regressions are used to model high-frequency responses by means of low-frequency variables. However, due to the periodic structure of RU-MIDAS regressions, the dimensionality grows quickly if the frequency mismatch between the high- and low-frequency variables is large. Additionally the number of high-frequency observations available for estimation decreases. We propose to counteract this reduction in sample size by pooling the high-frequency coefficients and further reduce the dimensionality through a sparsity-inducing convex regularizer that accounts for the temporal ordering among the different lags. To this end, the regularizer prioritizes the inclusion of lagged coefficients according to the recency of the information they contain. We demonstrate the proposed method on two empirical applications, one on realized volatility forecasting with macroeconomic data and another on demand forecasting for a bicycle-sharing system with ridership data on other transportation types.

econ.EM↗

arXiv2022

Spectral estimation for mixed causal-noncausal autoregressive models

This paper investigates new ways of estimating and identifying causal, noncausal, and mixed causal-noncausal autoregressive models driven by a non-Gaussian error sequence. We do not assume any parametric distribution function for the innovations. Instead, we use the information of higher-order cumulants, combining the spectrum and the bispectrum in a minimum distance estimation. We show how to circumvent the nonlinearity of the parameters and the multimodality in the noncausal and mixed models by selecting the appropriate initial values in the estimation. In addition, we propose a method of identification using a simple comparison criterion based on the global minimum of the estimation function. By means of a Monte Carlo study, we find unbiased estimated parameters and a correct identification as the data depart from normality. We propose an empirical application on eight monthly commodity prices, finding noncausal and mixed causal-noncausal dynamics.

econ.EM↗

arXiv2022

Inference in mixed causal and noncausal models with generalized Student's t-distributions

The properties of Maximum Likelihood estimator in mixed causal and noncausal models with a generalized Student's t error process are reviewed. Several known existing methods are typically not applicable in the heavy-tailed framework. To this end, a new approach to make inference on causal and noncausal parameters in finite sample sizes is proposed. It exploits the empirical variance of the generalized Student's-t, without the existence of population variance. Monte Carlo simulations show a good performance of the new variance construction for fat tail series. Finally, different existing approaches are compared using three empirical applications: the variation of daily COVID-19 deaths in Belgium, the monthly wheat prices, and the monthly inflation rate in Brazil.

econ.EM↗

arXiv2022

Is climate change time reversible?

This paper proposes strategies to detect time reversibility in stationary stochastic processes by using the properties of mixed causal and noncausal models. It shows that they can also be used for non-stationary processes when the trend component is computed with the Hodrick-Prescott filter rendering a time-reversible closed-form solution. This paper also links the concept of an environmental tipping point to the statistical property of time irreversibility and assesses fourteen climate indicators. We find evidence of time irreversibility in $GHG$ emissions, global temperature, global sea levels, sea ice area, and some natural oscillation indices. While not conclusive, our findings urge the implementation of correction policies to avoid the worst consequences of climate change and not miss the opportunity window, which might still be available, despite closing quickly.

econ.EM↗

arXiv2022

A short term credibility index for central banks under inflation targeting: an application to Brazil

This paper uses predictive densities obtained via mixed causal-noncausal autoregressive models to evaluate the statistical sustainability of Brazilian inflation targeting system with the tolerance bounds. The probabilities give an indication of the short-term credibility of the targeting system without requiring modelling people's beliefs. We employ receiver operating characteristic curves to determine the optimal probability threshold from which the bank is predicted to be credible. We also investigate the added value of including experts predictions of key macroeconomic variables.

econ.EM↗

arXiv2022

Detecting common bubbles in multivariate mixed causal-noncausal models

This paper proposes methods to investigate whether the bubble patterns observed in individual series are common to various series. We detect the non-linear dynamics using the recent mixed causal and noncausal models. Both a likelihood ratio test and information criteria are investigated, the former having better performances in our Monte Carlo simulations. Implementing our approach on three commodity prices we do not find evidence of commonalities although some series look very similar.

econ.EM↗

arXiv2022

Predicting crashes in oil prices during the COVID-19 pandemic with mixed causal-noncausal models

This paper aims at shedding light upon how transforming or detrending a series can substantially impact predictions of mixed causal-noncausal (MAR) models, namely dynamic processes that depend not only on their lags but also on their leads. MAR models have been successfully implemented on commodity prices as they allow to generate nonlinear features such as locally explosive episodes (denoted here as bubbles) in a strictly stationary setting. We consider multiple detrending methods and investigate, using Monte Carlo simulations, to what extent they preserve the bubble patterns observed in the raw data. MAR models relies on the dynamics observed in the series alone and does not require economical background to construct a structural model, which can sometimes be intricate to specify or which may lack parsimony. We investigate oil prices and estimate probabilities of crashes before and during the first 2020 wave of the COVID-19 pandemic. We consider three different mechanical detrending methods and compare them to a detrending performed using the level of strategic petroleum reserves.

econ.EM↗