TBA

“TBA”

Face to face 15.2.71 – Room 15.1.39

TBA

“TBA”

Face to Face 15.2.71 – Room 15.1.39

Tail Index Regression for Extremal Dependence” (joint work with Paulo M. M. Rodrigues from Banco de Portugal and NOVA School of Business and Economics)

“Tail Index Regression for Extremal Dependence” (joint work with Paulo M. M. Rodrigues from Banco de Portugal and NOVA School of Business and Economics)”

Face to Face Room 15.2.71 – Room 15.1.39

A Non-Crossing Quantile and Expected Shortfall Regression

“A Non-Crossing Quantile and Expected Shortfall Regression”

Abstract:

Recently proposed joint and two-step estimators for Expected Shortfall (ES) and Value-at-Risk (VaR) regressions often exhibit crossings of the estimated regression functions in finite samples, analogous to the classical quantile crossing problem. We propose an M-estimator for joint VaR and ES regression at multiple probability levels that prevents such crossings by incorporating non-crossing constraints into the optimization problem. We establish that, when crossings arise from finite-sample variability or mild model misspecification, the constrained estimator is asymptotically equivalent to its unconstrained counterpart, a result corroborated by simulation studies. The constraints can be imposed over either a subset or a superset of the covariate space, with the chosen domain acting as a regularization parameter that shrinks the regression functions toward common slopes. We illustrate the practical utility of the proposed method in two applications. First, in recently proposed macroeconomic regressions for Inflation-at-Risk, the non-crossing estimator not only eliminates crossings but also stabilizes parameter estimates and produces smoother predictions. Second, for forecasting VaR and ES of global financial indices using CAViaR-type models, imposing non-crossing constraints improves out-of-sample forecast performance compared to unconstrained CAViaR as well as classical benchmark models.

Face to face 15.2.71 – Room 15.1.39

Realized autoregressive conditional betas by Mariia Artemova, Christian Francq and Sébastien Laurent

Christian Francq

(ENSAE)

“Realized autoregressive conditional betas by Mariia Artemova, Christian Francq and Sébastien Laurent”

We propose a new model called RACB (Realized Autoregressive Conditional Beta) to model the dynamics of slope parameters (or betas) in a linear regression model with heteroscedastic errors. The proposed model is a quasi score-driven model obtained by modelling the joint distribution of the endogenous variable and the realized betas, conditional on the explanatory variables and under the assumption that the realized betas are unbiased estimators of the conditional betas.

The proposed model extends the Autoregressive Conditional Beta (ACB) model by conditioning the betas on lagged realized betas and by shrinking the conditional betas towards the realized betas.

We establish the key stochastic properties of the data generating process and the associated filter, and argue that the contraction condition for invertibility is not only sufficient but also almost necessary. We also show that when realized betas are not observed for certain observations, replacing them with the conditional betas is optimal in the Kullback–Leibler divergence sense.

Empirically, for 37 large U.S.\ stocks in a Fama–French three-factor setting, the RACB model achieves the best performance in a tracking portfolio exercise as it is the most frequently retained model in the Model Confidence Set.