Speakers of the JEF'2023 Conference (in alphabetical order)

Title: We modeled long memory with just one lag!

 (Paper ------ Slides*) 

Summary: We build on two contributions that have found conditions for large dimensional networks or systems to generate long memory in their individual components, and provide a multivariate methodology for modeling and forecasting series displaying long range dependence. We model long memory properties within a vector autoregressive system of order 1 and consider Bayesian estimation or ridge regression. For these, we derive a theory-driven parametric setting that informs a prior distribution or a shrinkage target. Our proposal significantly outperforms univariate time-series long- memory models when forecasting a daily volatility measure for 250 U.S. company stocks over twelve years. This provides an empirical validation of the theoretical results showing long memory can be sourced to marginalization within a large dimensional system. (Joint work with L. Bauwens and S. Laurent.)

Title: Practical estimation methods for high-dimensional multivariate stochastic volatility models

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Summary: We propose computationally inexpensive and efficient estimators for multivariate stochastic volatility (MSV) models with cross-dependence, Granger causality, and higher-order persistence in latent volatilities. The proposed class of estimators is based on a few moment equations derived from the VARMA representations of MSV models. Except for cross-dependence parameters, closed-form expressions for the other parameters are derived where no numerical optimization procedure or choice of initial parameter values is required. To increase the stability and efficiency of volatility persistence parameter estimates, we suggest shrinkage-type VARMA estimators where averaging or matrix-variate regression (MVR) is employed. We derive the asymptotic distribution of these estimators. Due to their computational simplicity, the VARMA estimators allow one to make reliable - even exact - simulation-based inferences by applying Monte Carlo test techniques. In empirically realistic setups, simulation results show that the proposed shrinkage estimator based on MVR is superior to Bayesian and QML estimators in terms of bias and root mean square error. We examine the precision of the shrinkage estimator using large-scale simulated data where models up to 1,500 dimensions and 4,503,000 parameters are fitted and studied. The proposed estimators are applied to stock return data, and the effectiveness of the proposed estimators is assessed in two ways. First, we show the usefulness of the proposed models and methods in estimating high-frequency returns with many assets and observations. Second, in the context of dynamic minimum variance portfolio strategy, we find that unrestricted higher-order MSV models outperform existing alternatives, including multivariate GARCH-type models. (Joint work with Md. Nazmul Ahsan.)

Title: Inference on GARCH-MIDAS models  without any small-order moment

 (Paper ------ Slides*) 

Summary: In GARCH-mixed-data sampling (GARCH-MIDAS) models, the volatility is decomposed into the product of two factors which  often received interpretations in terms of "short run" (high frequency) and "long run" (low frequency) components. While two-component volatility models are  widely used in applied works, some of their theoretical properties remain unexplored. We show that the strictly stationary solutions of such models do not admit any small-order finite moment, contrary to classical GARCH. It is shown that the strong consistency and the asymptotic normality of the Quasi-Maximum Likelihood estimator hold despite the absence of moments. Tests for the presence of a long-run volatility relying on the asymptotic theory and a bootstrap procedure are proposed. Our results are illustrated via Monte Carlo experiments and real financial data. (Joint work with B. M. Kandji and J-M Zakoïan.) 

Title: Long Run Risk in Stationary Structural Vector Autoregressive Models  

 (Paper ------ Slides*) 

Summary: This paper introduces a local-to-unity/small sigma process for a sta- tionary time series with strong persistence and non-negligible long run risk. This process represents the stationary long run component in an unobserved short- and long-run components model involving different time scales. More specifically, the short run component evolves in the calendar time and the long run component evolves in an ultra long time scale. We develop the methods of estimation and long run prediction for the univariate and multivariate Structural VAR (SVAR) models with unobserved components and reveal the impossibility to consistently es- timate some of the long run parameters. The approach is illustrated by a Monte-Carlo study and an application to macroeconomic data. (Joint work with J. Jasiak.)

Title: Taking advantage of biased proxies for forecast evaluation

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Summary: This paper studies the problem of assessing the predictive accuracy of different models when the variable of interest is observed with error. Since Patton (2011), forecasts have been compared using a class of loss function, leading to the true ranking when a conditionally unbiased proxy is used. However, conditionally unbiasedness often comes at the cost of increasing the noise of the proxy. We show that if bias and variances of proxies can be consistently estimated, a biased proxy is helpful to enhance the predictive accuracy comparison of two forecasts.

Title:  Inference on conditional systemic risk measures

 (Paper ------ Slides*) 

Summary: We propose a two-step semi-parametric estimation approach for dynamic Conditional VaR (CoVaR), from which other important systemic risk measures such as the Delta-CoVaR can be derived. The CoVaR allows to define reserves for a given financial entity, in order to limit exceeding losses when a system is in distress. We assume that all financial returns in the system follow conditional location-scale models, allowing us to derive an expression of the dynamic CoVaR as an affine function of a quantile of the innovations distribution and the first two conditional moments of the asset under consideration. Our estimation method relies on an equation-by-equation Quasi-Maximum Likelihood (QML) estimation of the dynamic models. We show that the dynamic systemic risk measures can be consistently estimated under mild assumptions. The study of the asymptotic behaviour of the estimators and the derivation of asymptotic confidence intervals for the dynamic CoVaR are the main purposes of the paper. Our theoretical results can be extended to a multi-asset setting, and are illustrated via Monte-Carlo experiments and real financial time series. (Joint work with Loïc Cantin and Christian Francq)  

Speakers of the HDDA-XII Workshop (in alphabetical order)

Title: Tests of multivariate exchangeability for high-dimensional data

 (Paper ------ Slides) 

Summary: Often in practice, same units are repeatedly observed under all experimental conditions, and simultaneous testing of mean vectors and covariance matrices for the resulting dependent data are required. For ex., same patients might be observed under drug and placebo, or expressions from normal and tumor cells are taken from same individuals. At a more general level, it pertains to testing for equal distributions, or exchangeability, of data vectors, since the group labels become arbitrary. The present work addresses this problem, where tests for multivariate exchangeability are constructed when the distributions may not necessarily be normal, particularly focusing on the case when the dimensions of parameters may exceed the sample size. Simple, computationally highly efficient, and consistent estimators are used to compose the test statistics. Simulation results are used to show the accuracy of the proposed tests. Applications on real data sets are also demonstrated. 

Title: Post-shrinkage strategies in high-dimensional data analysis 

 (Paper ------ Slides*) 

Summary: In high-dimensional settings where number of predictors is greater than observations, many penalized methods were introduced for simultaneous variable selection and  parameters estimation when the model is sparse. However, a model may have sparse signals as well as with number predictors with weak signals. In this scenario variable selection methods may not distinguish predictors with weak signals and sparse signals. The prediction based on a selected submodel may not be preferable in such cases. For this reason, we propose a high-dimensional shrinkage strategy to improve the prediction performance of a submodel. Such a high-dimensional shrinkage estimator (HDSE) is constructed by shrinking a weighted ridge estimator in the direction of a candidate submodel. We demonstrate that the proposed HDSE performs uniformly better than the weighted ridge estimator. Interestingly, it improves the prediction performance of given submodel generated from most existing variable selection methods. The relative performance of the proposed HDSE strategy is appraised by both simulation studies and the real data analysis. Some open research problems will be discussed, as well. 

Title: On Steinian Model Selection

 (Paper ------ Slides*) 

Summary: We use a consistent Stein risk estimator as an objective function with different constraints on shrinkage coefficients and on model parameters to obtain several tools for efficient selection of the parameters. The proposed class of threshold shrinkage estimators have explicit formulae and hence are intuitively interpretable. The asymptotic behavior of the estimators is investigated along with their ability to achieve reliable support recovery.

Title: Rates of convergence in Bayesian meta-learning

 (Paper ------ Slides*) 

Summary: The rate of convergence of Bayesian learning algorithms is determined by two conditions: the behavior of the loss function around the optimal parameter (Bernstein condition), the probability mass given by the prior to neighborhoods of the optimal parameter.

In meta-learning, we face multiple learning tasks, that are independent but are still expected to be related in some way. For example, the optimal parameters of all the tasks can be close to each other. It is then tempting to use the past tasks to build a better prior, that we use to solve future tasks more efficiently. From a theoretical point of view, we hope to improve the prior mass condition in future tasks, and thus, the rate of convergence. In this paper, we prove that this is indeed the case. Interestingly, we also prove that we can learn the optimal prior at a fast rate of convergence, regardless of the rate of convergence within the tasks (in other words, Bernstein condition is always satisfied for learning the prior, even when it is not satisfied within tasks).

This is joint work with Charles Riou (University of Tokyo and RIKEN AIP) and Badr-Eddine Chérief-Abdellatif (CNRS). The preprint is available: https://arxiv.org/abs/2302.11709

Title: Extreme expectile estimation for short-tailed data

 (Paper ------ Slides*) 

Summary: The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law- invariant coherent risk measures only consists of expectiles. While the theory of expectile estimation at central levels is substantial, tail estimation at extreme levels has so far only been considered when the tail of the underlying distribution is heavy. The article I will present is the first work to handle the short- tailed setting where the loss (e.g negative log-returns) distribution of interest is bounded to the right and the corresponding extreme value index is negative. We derive an asymptotic expansion of tail expectiles in this challenging context under a general second-order extreme value condition, which allows to come up with two semiparametric estimators of extreme expectiles, and with their asymptotic properties in a general model of strictly stationary but weakly dependent observations. A simulation study and a real data analysis from a forecasting perspective are performed to verify and compare the proposed competing estimation procedures.

Title: Sparse estimation in Markov regime-switching models

 (Paper ------ Slides*) 

Summary: Markov regime-switching vector auto-regressives are frequently used for modelling heterogeneous and complex relationships between variables in multivariate time series analysis. Applications include analyzing macroeconomic time series such as manufacturing activities, consumer price indices, and housing and asset prices. The most common method of estimation in these models is maximum likelihood estimation (MLE). However, even for moderate data dimension and number of regimes, the MLE becomes unstable. In this talk, we present regularization-based estimators when the number of regimes in the model is correctly or over-specified. We also discuss theoretical properties and finite-sample performance of the methods, including forecasting, and conclude with a real data analysis.  

Title: Optimality of Variational Inference for Stochastic Block Model

 (Paper ------ Slides*) 

Summary: Variational methods are extremely popular in the analysis of network data. Statistical guarantees obtained for these methods typically provide asymptotic normality for the problem of estimation of global model parameters under the stochastic block model. In the present work, we consider the case of networks with missing links that is important in application and show that the variational approximation to the maximum likelihood estimator converges at the minimax rate. This provides the first minimax optimal and tractable estimator for the problem of parameter estimation for the stochastic block model. We complement our results with numerical studies of simulated and real networks, which confirm the advantages of this estimator over current methods.

Title: Variable selection, monotone likelihood ratio and group sparsity

 (Paper ------ Slides*) 

Summary: In the pivotal variable selection problem, we derive the exact non-asymptotic minimax selector over the class of all s-sparse vectors, which is also the Bayes selector with respect to the uniform prior. While this optimal selector is, in general, not realizable in polynomial time, we show that its tractable counterpart (the scan selector) attains the minimax expected Hamming risk to within factor 2, and is also exact minimax with respect to the probability of wrong recovery. As a consequence, we establish explicit lower bounds under the monotone likelihood ratio property and we obtain a tight characterization of the minimax risk in terms of the best separable selector risk. We apply these general results to derive necessary and sufficient conditions of exact and almost full recovery in the location model with light tail distributions and in the problem of group variable selection under Gaussian noise.

This is joint work with Cristina Butucea,  Enno Mammen, and  Mohamed Ndaoud.