Université catholique de Louvain

IMMAQ

Institut de statistique, biostatistique et sciences actuarielles

Center for Operations Research and Econometrics

Convention ARC 07/12-002

Econometric modelling of multivariate financial time series

RAPPORT ANNUEL D’ETAT D’AVANCEMENT DES TRAVAUX

Période janvier 2011 – décembre 2011

Louvain-la-Neuve Mars 2012

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1. RENSEIGNEMENTS GENERAUX Convention ARC 07/12-002, « Econometric modelling of multivariate financial time series» Rapport d’état d’avancement des travaux pour l’année 2011. Promoteur(s) : Rainer VON SACHS, (main promotor), Professor Université catholique de Louvain, Institut de statistique, biostatistique et sciences actuarielles (ISBA) 20, Voie du Roman Pays, B-1348 Louvain-la-Neuve Tel.: +32-10-478806, Fax. : +32-10-473032 e-mail : rvs@uclouvain.be Luc BAUWENS, Professor, ECON, CORE and associated member of the Institut de statistique, biostatistique et sciences actuarielles (ISBA). Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 34, Voie du Roman Pays, B-1348 Louvain-la-Neuve Tel.: +32-10-474321, Fax.: +32-10-474301 e-mail : luc.bauwens@uclouvain.be Christian HAFNER, Professor, Université catholique de Louvain, Institut de statistique, biostatistique et sciences actuarielles (ISBA) and Center for Operations Research and Econometrics (CORE) 20, Voie du Roman Pays, B-1348 Louvain-la-Neuve Tel.: +32-10-474306, Fax. : +32-10-473032 e-mail : christian.hafner@uclouvain.be Johan SEGERS, Professor, Institut de statistique, biostatistique et sciences actuarielles (ISBA). 20, Voie du Roman Pays, B-1348 Louvain-la-Neuve Tél.: +32-10-474311, Fax. : +32-10-473032 e-mail : johan.segers@uclouvain.be Membres associés Sébastien Laurent, Professor, University of Maastricht, The Netherlands and CORE member. Sébastien Van Bellegem, Professor, Toulouse School of Economics, and CORE member. Dimitri Korobilis, Lecturer, University of Glasgow, Scotland, United Kingdom Michael Eichler, Professor, University of Maastricht, The Netherlands Jean-Marc Freyermuth, Postdoctoral researcher (since November 2011), KULeuven, Belgium Helmut Herwartz, Professor, University of Kiel, Germany Hans Manner, Professor, University of Cologne, Germany Giovanni Motta, Postdoctoral researcher, University of Maastricht, The Netherlands Jeroen Rombouts, Professor, HEC Montreal and Research associate of CORE, Quebec François Roueff, Professeur, Paris Tech (Ecole normale supérieure de Télécommunications), France

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Joseph Tadjuidje, Research associate, University of Kaiserslautern, Germany Francesco Violante, Postdoctoral researcher, University of Maastricht, The Netherlands 2. RENSEIGNEMENTS ADMINISTRATIFS A. Personnel - responsables des unités de recherche

Rainer von Sachs Président de l’IMMAQ Président de l’ISBA Université Catholique de Louvain 20, voie du Roman Pays Luc Bauwens Président du CORE CORE Université Catholique de Louvain 34, voie du Roman Pays François Maniquet Directeur de recherche CORE Université Catholique de Louvain 34, voie du Roman Pays Ingrid Van Keilegom Directrice de recherche ISBA Université Catholique de Louvain 20, voie du Roman Pays

- personnel à charge du programme (nom, prénom, qualification, statut, ETP, période d’occupation)

Ces informations sont reprises dans l’Annexe A du présent rapport.

- personnel non à charge mais travaillant sur les thèmes de l’ARC (nom, prénom, qualification, statut, période d’activité, pourcentage d’occupation)

Ces informations sont reprises dans l’Annexe B du présent rapport.

B. Autres contrats Contrat institutionnel IAP 06/03 pour les membres de l’Institut de statistique, biostatistique et sciences actuarielles Ch. Hafner, J. Segers et R. von Sachs.

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3. RENSEIGNEMENTS SCIENTIFIQUES 3.1. Résumé du projet et de son évolution, situé dans son contexte et 3.2. Description des travaux exécutés et de leurs résultats The research project is organized via a series of subprojects corresponding to the major areas of parametric, semi-parametric and non-parametric approaches as well as on more empirical research (“applications”). In what follows, applications are included in the three parts according to the tools that are used. A. Parametric approaches In this section we present our research on multivariate time series analysis using parametric approaches. Hafner and Manner (2011) provide a general overview of the current literature on empirical modeling of asset price processes, including dynamic volatility and copula models, while Bauwens, Hafner and Laurent (2012) is a new handbook of volatility modeling, covering classical models such as GARCH and Stochastic Volatility, but also more recent advances in realized volatility modeling. A.1. Modelling dependence between financial returns using copulas Copulas are used for dependence modelling, in particular for financial data. Hafner and Manner (2012) propose a new dynamic copula model where the parameter characterizing dependence follows an autoregressive process. As this model class includes the Gaussian copula with stochastic correlation process, it can be viewed as a generalization of multivariate stochastic volatility models. Despite the complexity of the model, the decoupling of marginals and dependence parameters facilitates estimation. The authors propose estimation in two steps, where first the parameters of the marginal distributions are estimated, and then those of the copula parameters of the latent processes (volatilities and dependence) are estimated using efficient importance sampling (EIS). They discuss goodness-of-fit tests and ways to forecast the dependence parameter. For two bivariate stock index series, they show that the proposed model outperforms standard competing models. Hafner (2012) uses a new concept in wavelet analysis to explore a financial transaction data set including returns, durations and volume. The concept is based on a decomposition of the Allan covariance of two series into cross-covariances of wavelet coefficients, which allows a natural interpretation of cross-correlations in terms of frequencies. It is applied to financial transaction data including returns, durations between transactions, and trading volume. At high frequencies, we find significant spill-over from durations to volume and a strong contemporaneous relation between durations and returns, whereas a strong causality between volume and volatility exists at various frequencies. A.2. Multivariate volatility models The availability of measures of daily variances of financial returns, and covariances between these, allows researchers to model time series of covariance matrices. One interest of these models is that they can be used for forecasting future values, which is typically of use in financial applications such as hedging, option pricing, risk management, and portfolio

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allocation. Another potential interest of models for realized covariance matrices is that they allow researchers to study the macroeconomic and financial determinants of the changes in multivariate volatility. GARCH models can be used for the same purposes than measures based on intraday data but, since they rely on daily observed returns, they provide less precise estimates and forecasts of variances and covariances. Bauwens, Storti and Violante (2012) propose a new dynamic model for realized covariance matrices, assuming a Wishart conditional distribution. The expected value of the realized covariance matrix is specified in two steps: a model for each realized variance, and a model for the realized correlation matrix. The realized variance model can be taken in the menu of existing univariate models. The realized correlation model is a dynamic conditional correlation model. Estimation is organized in two steps as well, and a quasi-ML interpretation is given to each step. Moreover, the model is applicable to large matrices since estimation can be done by the composite likelihood method. Hafner and Reznikova (2011) consider the estimation of the dynamic conditional correlation (DCC) model. It is now well recognized that the maximum likelihood estimator applied to the DCC model is severely biased in high dimensions and, in particular, in cases where the time series dimension is close to the sample size. In this paper, we argue that one of the reasons for the bias lies in an ill-conditioned sample covariance matrix, which is used in the so-called variance targeting technique to match sample and theoretical unconditional covariances. We propose to reduce the bias by using shrinkage to target methods for the sample covariance matrix. As targets we use, alternatively, the identity matrix, a single factor model, and equicorrelation. Since the shrinkage intensity decreases towards zero with increasing sample size, the estimator is asymptotically equivalent to the efficient maximum likelihood estimator. The finite sample performance of the proposed estimator over alternative estimators is demonstrated through a Monte Carlo study. Finally, we provide an illustrative application to financial time series. Hafner, Laurent and Violante (2011) derive the diffusion limit of dynamic conditional correlation models. For the standard DCC model, we provide a degenerated diffusion limit, while for a modified version of the DCC model, we show that a non-degenerated diffusion limit can be obtained. The diffusion matrix is of reduced rank due to collinearity of the innovations in the volatility and correlation dynamics. In an empirical application, we show that the distribution of realized correlations generated from high frequency DCC models can be recovered using our results. The deregulation of European electricity markets has led to an increasing need in understanding the volatility and correlation structure of electricity prices. Bauwens, Hafner, and Pierret (2011) model futures series of the European Energy Exchange (EEX) index, using an asymmetric GARCH model for volatilities and augmented dynamic conditional correlation (DCC) models for correlations. In particular, they allow for smooth changes in the unconditional volatilities and correlations through a multiplicative component that they estimate non-parametrically. They also introduce exogenous variables in the new multiplicative DCC model to account for congestion in short-term conditional volatilities. They find different correlation dynamics for long and short-term contracts and the new model achieves higher forecasting performance compared to a standard DCC model. Laurent, Rombouts and Violante (2011) address the question of the selection of multivariate GARCH models in terms of variance matrix forecasting accuracy with a particular focus on relatively large scale problems. They consider 10 assets from NYSE and NASDAQ and

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compare 125 models based one-step-ahead conditional variance forecasts over a period of 10 years using the model confidence set (MCS) and the Superior Predicitive Ability (SPA) tests. Model performances are evaluated using four statistical loss functions which account for different types and degrees of asymmetry with respect to over/under predictions. When considering the full sample, MCS results are strongly driven by short periods of high market instability during which multivariate GARCH models appear to be inaccurate. Over relatively unstable periods, i.e. dot-com bubble, the set of superior models is composed of more sophisticated specifications such as orthogonal and dynamic conditional correlation (DCC), both with leverage effect in the conditional variances. However, unlike the DCC models, the results show that the orthogonal specifications tend to underestimate the conditional variance. Over calm periods, a simple assumption like constant conditional correlation and symmetry in the conditional variances cannot be rejected. Finally, during the 2007-2008 financial crisis, accounting for non-stationarity in the conditional variance process generates superior forecasts. The SPA test suggests that, independently from the period, the best models do not provide significantly better forecasts than the DCC model of Engle (2002) with leverage in the conditional variances of the returns. In recent years multivariate models for asset returns have received much attention, in particular this is the case for models with time varying volatility. Rombouts and Stentoft (2011b) consider models of this class and examine their potential when it comes to option pricing. Specifically, they derive the risk neutral dynamics for a general class of multivariate heteroskedastic models, and they provide a feasible way to price options in this framework. Their framework can be used irrespective of the assumed underlying distribution and dynamics, and it nests several important special cases. They provide an application to options on the minimum of two indices. The results show that not only is correlation important for these options but so is allowing this correlation to be dynamic. Moreover, they show that for the general model exposure to correlation risk carries an important premium, and when this is neglected option prices are estimated with errors. Finally, they show that when neglecting the non-Gaussian features of the data, option prices are also estimated with large errors. Rombouts and Stentoft (2011a) use asymmetric heteroskedastic normal mixture models to fit return data and to price options. The models can be estimated straightforwardly by maximum likelihood, have high statistical fit when used on S&P 500 index return data, and allow for substantial negative skewness and time varying higher order moments of the risk neutral distribution. When forecasting out-of-sample a large set of index options between 1996 and 2009, substantial improvements are found compared to several benchmark models in terms of dollar losses and the ability to explain the smirk in implied volatilities. Overall, the dollar root mean squared error of the best performing benchmark component model is 39% larger than for the mixture model. When considering the recent financial crisis this difference increases to 69%. Van Dijk, Munandar and Hafner (2011) document the existence of large structural breaks in the unconditional correlations among the British pound, Norwegian krone, Swedish krona, Swiss franc, and euro exchange rates (against the US dollar) during the period 1994-2003. Using the framework of dynamic conditional correlation (DCC) models, we find that such breaks occurred both at the time the formal decision to proceed with the euro was made in December 1996 and at the time of the actual introduction of the euro in January 1999. In particular, we document that most correlations were substantially lower during the intervening period. We also find breaks in unconditional volatilities at the same points in time, but these are of a much smaller magnitude comparatively.

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B. Semi-parametric approaches B.1. Regime-switching models (see also C.3) The purely parametric approach to regime-switching can be explained as follows: a time series model (like a linear autoregressive model) is specified, and its parameters are allowed to change at relatively infrequent and unknown points of time. The mechanism driving the parameter changes is a (first order) discrete Markov chain, parameterized by a transition matrix. Each off-diagonal entry of the matrix corresponds to a probability of switching from one state (i.e. one value of the model parameters) to another state, while a diagonal entry corresponds to the probability to remain in a given state. A particular restriction on the structure of this matrix is interesting for time series models: in a given row, all values are equal to 0, except the diagonal value and the value preceding it. This means that if the system is in a given state, it can either stay in the same state or switch to the next state, but it cannot revert to a previous state. – Nonparametric approaches to regime-switching are treated in section C.3 where we consider a general model of mixtures of covariance matrices of time series portfolios in different hidden states. Bauwens and Rombouts (2011) consider the issue of estimating correctly the number of change points in this class of models. In Bayesian inference, the number of change points is typically chosen by the marginal likelihood criterion, computed by Chib’s method (Chib 1996). This method requires to select a value in the parameter space at which the computation is done. The authors in detail how to perform Bayesian inference for a change-point dynamic regression model and how to compute its marginal likelihood. Motivated by results from three empirical illustrations, a simulation study shows that Chib’s method is robust with respect to the choice of the parameter value used in the computations, among posterior mean, mode and quartiles. Furthermore, the performance of the Bayesian information criterion, which is based on maximum likelihood estimates, in selecting the correct model is comparable to that of the marginal likelihood. Bauwens, Koop, Korobilis and Rombouts (2011) compare the forecasting performance of different models which have been proposed for forecasting in the presence of structural breaks. These models differ in their treatment of the break process, the parameters defining the model which applies in each regime and the out-of-sample probability of a break occurring. In an extensive empirical evaluation involving many important macroeconomic time series, they demonstrate the presence of structural breaks and their importance for forecasting in the vast majority of cases. However, they find no single forecasting model consistently works best in the presence of structural breaks. In many cases, the formal modeling of the break process is important in achieving good forecast performance. However, there are also many cases where simple, rolling OLS forecasts perform well. Bauwens, Dufays and Rombouts (2011) develop a Markov Chain Monte Carlo algorithm to estimate Markov-switching GARCH and change-point GARCH models. These models are difficult to estimates due to the path dependence problem. Though Bauwens, Preminger and Rombouts (2010) had already developed an algorithm, the new one is more efficient and enables in addition to compute the marginal likelihood, which is essential for determining the number of regimes or change-points. The new algorithm is a particle MCMC one, a technique proposed by Andrieu et al. (2010). The authors illustrate the performance of the new algorithm on simulated and real data.

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Bauwens, de Backer and Dufays (2011) develop an algorithm, based on a differential evolution MCMC method, for Bayesian inference in AR-GARCH models subject to an unknown number of structural breaks at unknown dates. Break dates are directly treated as parameters and the number of breaks is determined by the marginal likelihood criterion. The authors prove the convergence of the algorithm and show how to compute marginal likelihoods. They allow for both pure change-point and recurrent regime specifications and show how to forecast structural breaks. They illustrate the efficiency of the algorithm through simulations and they apply it to eight financial time series of daily returns over the period 1987-2011. B.2. Time-varying parametric models A general modeling approach that combines the advantages of parametric and nonparametric approaches is to consider familiar parametric time series models such as ARMA or GARCH, and then allow the parameters to smoothly change over time. Under some general conditions, such models can be considered as locally stationary, in the sense that locally they have a behavior similar to stationary processes. Manner and Reznikova (2012) present an overview of copula models with time-varying parameters. The time dependence can be achieved by letting the parameters follow stochastic processes, or by specifying them as smoothly changing functions of time. In the latter case, the model is, under technical conditions, locally stationary and can be estimated by local maximum likelihood. Bocart and Hafner (2011) suggest a new heteroskedastic hedonic regression model that takes into account time-varying volatility and is applied to a blue chips art market. Furthermore, they use a semi-parametric local likelihood estimator that is more precise than the often used dummy variables method. The empirical analysis reveals that errors are considerably non-Gaussian, and that a student distribution with time-varying scale and degrees of freedom does well in explaining deviations of prices from their expectation. The art price index is a smooth function of time and has a variability that is comparable to the volatility of stock indices. In a semi-parametric approach to spectral density estimation, hence avoiding fitting a parametric model such as AFRIMA, Roueff and von Sachs (2011) estimate the long-memory parameter d of a strongly dependent (financial) time series by a variant of a recent wavelet method. Hereby this parameter d, specifying the spectral behaviour at zero frequency, i.e. the persistence of long-range dependency, is allowed to vary over time, as is the non-parametric part of the spectral density. We embed our approach in the framework of locally stationary processes, which has been developed essentially for weakly dependent time series with a time-varying spectral structure. We show weak consistency and a central limit theorem for our log-regression wavelet estimator of the time-dependent d in a Gaussian context. We apply our method to a series of exchange rates which reveals periods of changing amplitude of the long-memory parameter d. Moreover some simulation studies confirm the good performance of our estimator which can be considered to follow a fairly general approach, in contrast to the few existing parametric approaches.

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C. Non-parametric approaches C.1. Heavy-tailed time series When a spatial process is recorded over time and the observation at a given time instant is viewed as a point in a function space, the result is a time series taking values in a Banach space. To study the spatio-temporal extremal dynamics of such a time series, the latter is typically assumed to be jointly regularly varying. In Meinguet and Segers (2010), this assumption is shown to be equivalent to convergence in distribution of the rescaled time series conditionally on the event that at a given moment in time it is far away from the origin. The limit is called the tail process or the spectral process depending on the way of rescaling. These processes provide convenient starting points to study, for instance, joint survival functions, tail dependence coefficients, extremograms, extremal indices, and point processes of extremes. In Meinguet (2011), an estimation algorithm is proposed for fitting a new class of heavy-tailed models for spatio-temporal dependence coined 'CM3', maxima of moving maxima of continuous functions. The spectral processes from this class admit particularly simple expressions. Furthermore, CM3 processes fulfill the finite-cluster condition and the strong mixing condition. C.2. Inference on copulas and tail dependence Correlation mixtures of elliptical copulas arise when the correlation parameter is driven itself by a latent random process, as for instance in the SCAR model proposed in Hafner and Manner (2012). In Manner and Segers (2011), both penultimate and asymptotic tail dependence of such copulas are found to be much larger than for ordinary elliptical copulas with the same unconditional correlation. Furthermore, for Gaussian and Student t-copulas, tail dependence at sub-asymptotic levels is generally larger than in the limit, which can have serious consequences for estimation and evaluation of extreme risk. Finally, although correlation mixtures of Gaussian copulas inherit the property of asymptotic independence, at the same time they fall in the newly defined category of near asymptotic dependence. The consequences of these findings for modeling are assessed by means of a simulation study and a case study involving financial time series. The article by Guillotte, Perron and Segers (2011) must be the first paper where Bayesian nonparametrics are set to work in extreme-value theory. The Bayesian paradigm is attractive as it provides a coherent way to combine various sources of information (objective and subjective) with the task of delivering a single object, the predictive distribution, that incorporates both process and estimation uncertainty. Nonparametrics are needed as parametric assumptions are to be avoided as much possible when it comes to extrapolation. A classical, frequentist approach is favored in Einmahl, Krajina and Segers (2011) for the general multivariate case. By employing a method-of-moments approach, smoothness assumptions are minimised, making the methodology applicable to distributions with discrete spectral measures, to be interpreted as factor models for extremes.

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Tail dependence can also be modelled via a special class of multivariate probability distributions, called extreme-value copulas. For work on this topic by Johan Segers' PhD student Gordon Gudendorf, please see the corresponding section 3.3. In Kojadinovic, Segers and Yan (2011), nonparametric tests are proposed for the hypothesis that the copula of a multivariate distribution is an extreme-value copula. The test is based on the characterisation of such copulas via max-stability. In contrast to previous methods, the test is applicable in an arbitrary number of dimensions. In order to calculate critical values of the test, resampling methods based on the multiplier central limit theorem are used. In Segers (2011a), a counter-example is given to the claim that a bivariate Archimedean copula is determined by its diagonal section. The example serves as a warning that the conjecture that multivariate Archimedean copulas are determined by their Kendall distribution functions must not be taken too lightly. The mathematical object underlying most of the afore-mentioned contributions is the empirical copula process. Weak convergence of this process under minimal smoothness assumptions is considered in Segers (2011b). C.3. Shrinkage estimation for Hidden Markov regime switching In Böhm and von Sachs (2009), and also in Hafner and Reznikova (2011), cf Section A.2, shrinkage has been investigated as a remedy against numerical instabilites due to deteriorating condition numbers of estimators of multivariate spectral or covariance matrices, respectively. This idea of regularization by shrinkage of a high-dimensional covariance matrix towards a multiple of the identity matrix has been applied by Franke, Fiecas, von Sachs and Tadjudje (2011) in the context of nonparametric covariance estimation of a multivariate portfolio in the presence of two or several hidden Markov states. It is shown that both maximum-likelihood estimation (via an EM-algorithm) and reconstruction of the hidden path is drastically stabilized in the presence of shrinkage which is in particular interesting in the context of rarely visited states due to a small effective sample size compared to the dimensionality of the panel. C.4. Time-varying factor models The factor model approach is a prominent approach for modeling the superimposing effects of common and individual behavior of multiple macroeconomic data, such as market indices, GDP, unemployment, etc. As soon as the dimension N of such multivariate data becomes large (and possibly large compared to the length T of the data), the question of reducing dimensionality arises: can one describe the data by a small number d < N of common factors? And how can this number, and the corresponding factors be identified (estimated) from the data? As empirical analysis of ours has shown, there is strong evidence that it is unrealistic to assume the second-order structure of these macroeconomic data does not change over time - which is plausible in view of economic crisis, changing policies of central banks, and alike. In the published work by Motta, Hafner and von Sachs (2011) we treat, as first instance, static factor models with smoothly over time changing loadings. We develop a local version of Principal Components Regression, and we show, in the theoretical framework of both cross-

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sectional dimension N and length T of the data tending to infinity, consistency of our estimators of the loadings and of the factors. Our simulation studies confirm these theoretical results from the empirical side. With this work, we have truly generalized the time-constant static approach developed in Bai and Ng (2002) by embedding it into the framework of local stationarity. The paper Eichler, Motta and von Sachs (2011) treats dynamic factor models. As such it renders time-varying the dynamic but time-homogeneous model of Forni, Hallin, Lippi and Reichlin (2000): the common factors (or "shocks") are allowed to be of locally-stationary nature, and more particularly the factor loading coefficients are time-varying filters. We also allow for locally-stationary idiosynchratics. This amounts to model the complete dynamic structure time-variant. By a localized principal components approach in the frequency domain, using again a double asymptotic framework, we develop a weakly consistent estimator of the common components of the factor model. Hereby we solve a variety of conceptional problems on locally stationary filtering and on uniform consistency of empirical principal components in the frequency domain. C.5 Nonparametric spectral estimation In Bouezmarni and Van Bellegem (2011), a new nonparametric spectral density estimator is introduced via smoothing the periodogram by the probability density of a Beta random variable (Beta kernel). The estimator is proved to be bounded for short memory data, and diverges at the origin for long memory data. The convergence in probability of the relative error and Monte Carlo simulations suggest that the estimator automatically adapts to the long- or the short-range dependency of the process. A cross-validation procedure is also studied in order to select the nuisance parameter of the estimator. Illustrations on historical as well as most recent returns and absolute returns of the S&P500 index show the reasonable performance of the procedure and show that the data-driven estimator is a valuable tool for the detection of long memory as well as hidden periodicities in stock returns. For contributions on tree-structured wavelet estimation, with applications on adaptively smoothing the possibly time-varying spectral structure of univariate and multivariate time series, please see the section 3.3, on PhD student J.-M. Freyermuth. 3.3. Présentation synthétique des travaux effectués par chaque doctorant à charge de la convention ARC Chercheur: Arnaud Dufays (Promoteur: Luc Bauwens, sujet: Volatility models with changing regimes) Objectif général de la recherche: Reliable forecasting is essential for good decision making for financial decisions related to asset allocations, risk evaluation, and hedging of risky investments. The prediction of the volatility of financial time series is usually done by a GARCH (Generalized Auto-Regressive Conditional Heteroskedastic) model. However the GARCH model with fixed parameters produces bad forecasts when it faces a structural change due to a changing environment or behaviour of agents of the economic system. As a consequence, an important econometric challenge is to detect as soon as possible a structural break. A useful modeling approach to

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capture breaks is the Markov-switching modeling framework. Important problems remain when we deal with Markov switching GARCH models. The most difficult issue is called the path dependence problem. It implies that maximum likelihood estimation is out of reach. Two very recent papers using Bayesian inference have proposed ways to solve this problem. However these recent algorithms are not sufficiently efficient to be used by practitioners. Moreover these approaches do not cover the multivariate modeling. The project is to continue this research and its global objective is to introduce efficient algorithms for the estimation of univariate and multivariate Markov-switching GARCH models. Travaux réalisés: Bauwens, Dufays and Rombouts (2011) develop a Markov Chain Monte Carlo algorithm to estimate Markov-switching GARCH and change-point GARCH models. These models are difficult to estimates due to the path dependence problem. Though Bauwens, Preminger and Rombouts (2010) had already developed an algorithm, the new one is more efficient and enables in addition to compute the marginal likelihood, which is essential for determining the number of regimes or change-points. The new algorithm is a particle MCMC one, a technique proposed by Andrieu et al. (2010). The authors illustrate the performance of the new algorithm on simulated and real data. Bauwens, de Backer and Dufays (2011) develop an algorithm, based on a differential evolution MCMC method, for Bayesian inference in AR-GARCH models subject to an unknown number of structural breaks at unknown dates. Break dates are directly treated as parameters and the number of breaks is determined by the marginal likelihood criterion. The authors prove the convergence of the algorithm and show how to compute marginal likelihoods. They allow for both pure change-point and recurrent regime specifications and show how to forecast structural breaks. They illustrate the efficiency of the algorithm through simulations and they apply it to eight financial time series of daily returns over the period 1987-2011. Projets pour 2012: Two projects are on the agenda. GARCH models with fixed parameters are too restrictive. However the path dependence problem does not allow direct estimation of the posterior distribution for more flexible models such as Markov-switching-GARCH models. This project will rely on a previous research, namely the Particle MCMC, that circumvents the path dependence problem. He will investigate a new Markov-switching GARCH model based on an infinite hidden Markov chain. The MCMC sampler will endogenously determine the number of regimes. The study will ultimately give some clues to the question whether a MS-GARCH model or a CP-GARCH model is better fitting a particular series. Multivariate GARCH type volatility models with fixed parameters are too restrictive for long time series due to breaks in the volatility process. These features result typically in artificially highly persistent processes when fitted and may produce unrealistic long term volatility forecasts. This project will propose a multivariate Change-point GARCH model of the dynamic conditional correlations type. This will allow to first detect breaks in the individual time series, and second in the conditional correlations. The model will be

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estimated using the D-DREAM, a novel algorithm that can deal with the path dependence problem, and the number of regimes will be estimated by maximizing the marginal likelihood. Chercheur: Jean-Marc Freyermuth (Thèse défendue le 20 octobre 2011, promoteur: Rainer von Sachs, sujet: Tree-structured wavelets in nonparametric function estimation) Objectif général de la recherche : The thesis of Jean-Marc Freyermuth (defended on October 20, 2011) treats research on a fundamental methodology of adaptive curve smoothing (denoising) by modern wavelet technology. Applications are numerous, in one and in higher dimensions: nonparametric regression, density and spectral density estimation, and alike, and in particular, estimation of the possibly time-varying second-order structure of univariate and multivariate time series, e.g. in the context of time series panels: if a spatially inhomogeneous spectrum of a locally stationary process has to be estimated in the time-frequency domain, existing methods of adaptively choosing the appropriate smoothing parameter over time and frequency fail due to either too much variability or too little adaptation. A similar problem exists in the context of estimation of a high-dimensional spectral matrix of a time series panel, prior to fitting a low-dimensional factor model to the data. Jean-Marc Freyermuth, in his thesis, has studied tree-structured wavelet (TSW) methods to answer these questions both from quite a general theoretical but also a quite applied point of view - with broad applications in areas such diverse as mixed effects modeling for time series panels, treated successfully in Freyermuth, Ombao and von Sachs (2010) on laying down the methodology. Travaux réalisés in 2011: In 2011, Jean-Marc Freyermuth has accomplished a series of projects on investigating the theoretical properties of his methodology, with the objective to understand in which situations tree-structured wavelet estimators are superior to existing wavelet thresholding schemes. A first theoretical work, published by Autin, Freyermuth and von Sachs (2011a), uses the maxiset approach (as in Autin, 2008) to show that for a specific new “hard-tree” thresholding scheme the largest class of functions to be successfully estimated by the given estimation procedure with a given rate of convergence is larger than for existing tree-thresholding and also for classical hard-thresholding schemes. Conclusions of this first theoretical paper suggest that future research for the best method among the VBT family would simultaneously optimize on the choice of the thresholding rule and on a method-dependent threshold value. Such kind of result for the VBT family is highly non trivial but first steps towards such a result have been derived in Autin, Freyermuth, and von Sachs (2011b) for the family of non-overlapping horizontal block thresholding (HBT) methods. It turns out that the best choice amounts to use the squared average of the empirical wavelet coefficients compared to a threshold which is of about the same order of magnitude as its variance. In a final paper, Autin, Freyermuth and von Sachs (2011c), the following question is answered. Is it possible to optimize the method within the family of either TSW or HBT methods? This question is a perfect illustration of the well known problem of selecting the ’best estimator’ among a too rich family of candidates. Based on the maxiset approach it is shown that it is not possible to compare TSW and HBT methods. The problem is resolved by

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proposing to combine these estimators. The resulting new estimator is proved to outperform each of its constituents from both a theoretical and a practical point of view, and the limitations of the proposed methodology are studied as well. The research of this thesis has stimulated quite a series of ongoing projects treating remaining open questions such as yet finer characterizations of function spaces well estimated by TSW-methods or generalizations of the methodology for higher dimensions, highly pertinent for applications. Jean-Marc Freyermuth has been hired as a postdoc at the KU Leuven, and will remain a research associate to this ARC project. Chercheur: Gordon Gudendorf (Promoteur: Johan Segers; sujet: "Extreme Value Analysis: Modelling Dependence between Many Variables") Objectif général de la recherche: Extreme-value analysis can be broadly described as the branch of statistics that focuses on the inference on a probability distribution at or near the frontier of its support. An important current-day topic in extreme-value analysis is the modelling of dependence between extremes, sometimes called tail dependence. The question is whether the occurrence of an unusually large value in one variable makes it more or less likely that something similar will happen for another variable, either at the same moment in time or in the (near) future. Tail dependence can be modelled via a special class of multivariate probability distributions, called extreme-value copulas. These mathematical objects are described by their Pickands dependence function (Capéràa, Fougères and Genest 1997). This function can be thought of as an infinite-dimensional (functional) parameter capturing all aspects of tail dependence. Aim of the project is to provide efficient, nonparametric estimators for the Pickands dependence function of an extreme-value copula. The interest is in particular in the case where the number of variables is large. This is in contrast with most of the literature, which is limited to the bivariate case. Travaux réalisés: In Gudendorf and Segers (2010), a survey is given of the state-of-the-art in dependence modeling via extreme-value copulas. Both probabilistic and statistical issues are reviewed, in a nonparametric as well as a parametric context. This paper has published in the proceedings of the Workshop on Copula Theory and its Applications (Warsaw, September 2009).

In Capéràa et al. (1997), a simple and quite efficient estimator of a bivariate extreme-value copula has been presented for the bivariate case, the asymptotic behavior of which has been established in Genest and Segers (2009). In Gudendorf and Segers (2011a, 2011b), multivariate extensions are provided of this and other rank-based nonparametric estimators of the Pickands dependence function. Following Fils-Villetard et al. (2008), the shape constraint that the estimator should itself be a Pickands dependence function is enforced by replacing an initial estimator by its best least-squares approximation in the set of Pickands dependence functions having a discrete spectral measure supported on a sufficiently fine grid. Weak convergence of the standardized estimators is demonstrated and the finite-sample performance of the estimators is investigated by means of a simulation experiment.

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Another way to enforce the shape constraints on an estimator of the Pickands dependence is through pseudo-maximum likelihood estimation via sieves. In the bivariate case, modelling a Pickands dependence function via B-splines is found to be a promising avenue.

Gordon Gudendorf is expected to defend his thesis in the summer of 2012.

Chercheur : Diane Pierret (Promoteurs : Luc Bauwens et Christian Hafner, sujet : Econometric Analysis and Risk Management in Energy Markets) Objectif général de la recherche: The research project aims at understanding and measuring the market risks faced by agents involved in the power industry when constructing their energy portfolio over time. Risk measures are based on conditional joint density forecasts of the portfolio returns. This conditional distribution relies on a statistical model where the concept of dependence is central. Portfolio allocation, risk measures and hedging strategies could be significantly improved by taking into account the dynamic dependence structure of energy prices. Most of the econometric literature on power prices has focused on modeling the behavior of the univariate and multivariate mean of spot price series. Haldrup and Nielsen (2006) suggest a Markov regime-switching model with three regimes to reflect directional congestion. De Jong and Schneider (2009) analyze cointegration between gas and power spot prices. Bosco et al. (2010) analyze the interdependencies between power spot prices of six European markets. We are interested in modeling the co-movements in the mean, in the variance and in the tails of a larger basket of financial products based on different underlying energies with various maturities and delivery periods, and traded across physically interconnected markets. Ultimately, we target to achieve higher forecasting performance and higher accuracy of risk measures in order to respond to the information needs of energy ‘investors’. Travaux réalisés: In Bauwens, Hafner and Pierret (2011), we model a multivariate futures series of the European Energy Exchange (EEX) index, using an asymmetric GARCH model for volatilities and augmented dynamic conditional correlation (DCC) models for correlations. In particular, we allow for smooth changes in the unconditional volatilities and correlations through a multiplicative component that we estimate non-parametrically. We also introduce exogenous variables in our new multiplicative DCC model to account for congestion in short-term conditional volatilities. We find different correlation dynamics for long and short-term contracts and the new model achieves higher forecasting performance compared to the standard DCC model of Engle (2002). Projets pour 2012: In a project on new risk measures in energy markets, we investigate the concept of systemic risk in the energy market and propose a new methodology to measure it. By analogy with financial markets, the energy market is regarded as a sector that supports the whole economy. Common movements in energy assets are analyzed through measures of causality, common factor exposure and sensitivity to extreme market events. We find evidence of linear and non-linear causality among the daily returns of energy assets and an industrial index. After removing causal relationships, we estimate the dynamic exposure to common latent factors based on a principal component analysis of time-varying correlations. The systemic risk

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sensitivity of each asset is estimated with the Marginal Expected Shortfall (MES) capturing the tail dependence between the asset and the first common factor interpreted as the energy market index. Liste des références : Andrieu C., Doucet A. and R. Holenstein (2010). Particle Markov chain Monte Carlo methods. Journal of the Royal Statistical Society, 72, 269-342. Autin, F. (2008). On the performances of a new thresholding procedure using tree structure. Electronic Journal of Statistics 2, 412-431. Autin, F., Freyermuth, J.-M. and R. von Sachs (2011a). Ideal denoising within a family of tree-structured wavelet estimators. ISBA DP 2011-02 and Electronic Journal of Statistics 5, 829-855. Autin, F., Freyermuth, J.-M. and R. von Sachs (2011b). Block-threshold-adapted estimators via a maxiset approach. ISBA DP 2011-17 Autin, F., Freyermuth, J.-M. and R. von Sachs (2011c). Combining thresholding rules: a new way to improve the performance of wavelet estimators. ISBA DP 2011-21 Bai, J. and S. Ng (2002). Determining the number of factors in approximate factor models. Econometrica. 70, 191-221. Bauwens, L., Hafner, C.M. and Laurent, S. (2012), Handbook of Volatility Models and Their Applications, Wiley, forthcoming. Bauwens, L., Hafner, C.M. and D. Pierret (2011), Multivariate volatility modeling of electricity futures, Journal of Applied Econometrics, forthcoming. Bauwens, L., Koop, G., Korobilis, D. and J.V.K. Rombouts (2011) A comparison of forecasting procedures for macroeconomic series: the contribution of structural break models, CORE DP 2011-03. Bauwens, L., Preminger, A. and J.V.K. Rombouts (2010), Theory and inference for a Markov switching GARCH model - The Econometrics Journal, 13, 218 - 244. Bauwens, L. and J.V.K. Rombouts (2011), On marginal likelihood computation in change-point models - Computational Statistics and Data Analysis, Forthcoming. Bauwens L., Dufays A. and J.V.K. Rombouts (2011). Marginal likelihood for Markov-switching and change point GARCH models. CORE DP 2011/13. Bauwens, L., De Backer, B. and A. Dufays (2011) Estimating and forecasting structural breaks in financial time series CORE DP 2011/55

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Bauwens, L., Storti, G., and Violante, F. (2012). CAW-DCC: a dynamic model for vast realized covariance matrices. Forthcoming CORE DP. Bocart, F. and Hafner, C. (2012) Econometric analysis of volatile art markets, Computational Statistics and Data Analysis, forthcoming. Böhm, H. and R. von Sachs (2009). Shrinkage estimation in the frequency domain of multivariate time series. Journal of Multivariate Analysis. 100, 913-935. Bosco, B., Parisio, L., Pelagatti, M. and F. Baldi (2010), Long-run relations in European electricity prices - Journal of Applied Econometrics, 25, 805–832. Bouezmarni, T. and S. Van Bellegem (2011), Nonparametric Beta Kernel Estimator for Long Memory Time Series, CORE DP 2011-04, submitted and under revision. Capéràa, P., Fougères, A.-L. and C. Genest (1997), A nonparametric estimation procedure for bivariate extreme value copulas, Biometrika 84, 567-577. Chib S. (1996). Calculating posterior distribution and modal estimates in markov mixture models. Journal of Econometrics, 75:79–97. De Jong, C. and S. Schneider, (2009). Cointegration between gas and power spot prices - The Journal of Energy Markets, 2(3), 27–46. Dufays A. and De Backer B. (2011). Change-point GARCH models and marginal likelihood computation using discrete differential evolution Monte Carlo. Mimeo.

Eichler, M., Motta, G. and R. von Sachs (2011), Fitting dynamic factor models to non-stationary time series - Journal of Econometrics, Special Issue on "Factor Structures for Panel and Multivariate Time Series Data", 163, 51-70, 2011.

Einmahl, J.H.J., Krajina, A. and J. Segers (2011) An M-estimator for tail dependence in arbitrary dimension, ISBA DP 2011-05. Engle, R.F. (2002), Dynamic conditional correlation: a simple class of multivariate generalized autoregressive conditional heteroskedasticity models - Journal of Business and Economic Statistics, 20(3), 339–350. Fils-Villetard, A., Guillou, A. and Segers, J. (2008) "Projection estimators of Pickands dependence functions", The Canadian Journal of Statistics, 36, 369-382. Forni, M., Hallin, M., Lippi, M. and L. Reichlin (2000). The generalized dynamic factor model: identification and estimation. Review of Economics and Statistics. 82, 540-554. Franke, J., Fiecas, M., von Sachs, R. and J. Tadjuidje (2011). Shrinkage estimation for multivariate Hidden Markov mixing models. Mimeo.

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Freyermuth, J.-M., Ombao, H. and R. von Sachs (2010), Tree-structured wavelet estimation in a mixed effects model for spectra of replicated time series - Journal of the American Statistical Association, 105, 490, 634-646. Freyermuth, J.-M. (2011), Tree-Structured Wavelets in Nonparametric Function Estimation, ISBA, UCL thesis 2011. Genest, C. and Segers, J. (2009), Rank-based inference for bivariate extreme-value copulas, The Annals of Statistics 37, 2990-3022. Gudendorf, G. and J. Segers (2010), "Extreme-value copulas" - Copula Theory and its applications (Warsaw, 2009) (Jaworski, P., Durante, F., Härdle, W. and Rychlik, W. eds). Lecture Notes in Statistics - Proceedings, Springer-Verlag, Berlin, 127-146. Gudendorf, G. and J. Segers (2011a), Nonparametric estimation of an extreme-value copula in arbitrary dimensions - Journal of Multivariate Analysis, 102:7-47. Gudendorf, G. and J. Segers (2011b), Nonparametric estimation of multivariate extreme-value copulas, ISBA DP 2011-18. Guillotte, S., Perron F. and J. Segers (2011), Nonparametric Bayesian inference on bivariate extremes - Journal of the Royal Statistical Society, Series B, 73, 377-406. Hafner, C.M. (2012), Cross-correlating wavelet coefficients with applications to high frequency financial time series, Journal of Applied Statistics, forthcoming. Hafner, C.M. and H. Manner (2011), Multivariate time series models for asset prices - Handbook of Computational Finance, Springer Verlag, forthcoming. Hafner, C.M. and H. Manner (2012), Dynamic stochastic copula models: Estimation, inference and applications - Journal of Applied Econometrics, 27 (2), 269–295. Hafner, C.M. and O. Reznikova (2011), On the estimation of dynamic conditional correlation models - Computational Statistics and Data Analysis, forthcoming. Hafner, C.M. and Shin-Huei Wang (2011), Estimating autocorrelations in the presence of deterministic trends - Journal of Time Series Econometrics, 3, 1–23. Hafner, C.M., Laurent S. and F. Violante (2011). The diffusion limit of dynamic conditional correlation models. ISBA DP, UCL, forthcoming. Haldrup, N. and M. Nielsen (2006), Directional congestion and regime switching in a long memory model for electricity prices - Studies in Nonlinear Dynamics & Econometrics, 10(3), article 1, 2006. Kojadinovic, I., Segers, J. and Yan, J. (2011), Large-sample tests of extreme-value dependence for multivariate copulas, The Canadian Journal of Statistics, 39, 97-111. Laurent, S., Rombouts, J.V.K. and F. Violante (2011), On the forecasting accuracy of multivariate GARCH models, CORE DP 2010-25, submitted and under revision.

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Manner, H. and O. Reznikova (2012), Time-varying copulas: a survey, Econometric Reviews, 31, 654-687. Manner, H. and J. Segers (2011), Tails of correlation mixtures of elliptical copulas, Insurance: Mathematics and Economics, 48, 153-160. Meinguet, T. (2011), Maxima of moving maxima of continuous functions, Extremes, DOI 10.1007/s10687-011-0136-8. Meinguet, T. and J. Segers (2010), Regularly varying time series in Banach spaces, ISBA DP 2010-02, submitted and under revision. Motta, G., Hafner, C.M. and R. von Sachs (2011), Locally stationary factor models: identification and nonparametric estimation, Econometric Theory, 27 (6), 1279-1319. Rombouts, J.V.K. and L. Stentoft (2011a), Option pricing with asymmetric heteroskedastic normal mixture models, CORE DP 2010-49, submitted and under revision. Rombouts, J.V.K. and L. Stentoft (2011b), Multivariate option pricing with time varying volatility and correlations. Journal of Banking and Finance, forthcoming. Roueff, F. and R. von Sachs (2011), Locally stationary long memory estimation - Stochastic Processes and their Applications, 121, 813-844.

Segers, J. (2011a), Comments on Inference in multivariate Archimedean copula models - Test, An Official Journal of the Spanish Society of Statistics and Operations Research, 19, 1, 2011.

Segers, J. (2011b), Asymptotics of empirical copula processes under nonrestrictive smoothness assumptions, Bernoulli, forthcoming.

Van Dijk, D., Munandar, H., and C.M. Hafner (2011), The Euro-introduction and non-Euro currencies, Applied Financial Economics, 21, 95-116. 3.4. Liste des publications et rapports effectués durant cette période 3.4.1. Liste des prépublications (discussion papers, technical reports, mimeo) Autin, F., Freyermuth, J.-M. and R. von Sachs (2011a) Ideal denoising within a family of tree-structured wavelet estimators ISBA DP 2011-02 and Electronic Journal of Statistics, 5, 829-855, 2011. Autin, F., Freyermuth, J.-M. and R. von Sachs (2011b) Block-Threshold-Adapted Estimators via a maxiset approach ISBA DP 2011-17 Autin, F., Freyermuth, J.M. and R. von Sachs (2011c) Combining thresholding rules: a new way to improve the performance of wavelet estimators ISBA DP 2011-21

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Bauwens, L., De Backer, B. and A. Dufays (2011) Estimating and forecasting structural breaks in financial time series CORE DP 2011/55 Bauwens L., Dufays A. and J.V.K. Rombouts (2011) Marginal likelihood for Markov-switching and Change-Point GARCH models CORE DP 2011-13 Bauwens, L., Hafner, C.M. and S. Laurent (2011) Volatility models. CORE DP 2011/58. Forthcoming in: L. Bauwens, C. Hafner and S. Laurent (Eds.), Handbook of Volatility Models and their Applications, John Wiley & Sons. Bauwens, L., Hafner, C.M. and D. Pierret (2011) Multivariate volatility modeling of electricity futures CORE DP 2011-11 & ISBA DP 2011-13. Forthcoming in Journal of Applied Econometrics. Bauwens, L., Koop, G., Korobilis, D. and J.V.K. Rombouts (2011) A comparison of forecasting procedures for macroeconomic series: the contribution of structural break models, CORE DP 2011-03 Bauwens, L. and D. Korobilis (2011) Bayesian methods. CORE DP 2011-61. Forthcoming in: N. Hashimzade and M. Thornton (Eds.), Handbook of Research Methods and Applications on Empirical Macroeconomics, Edward Elgar Publishing. Bocart, F. and C. M. Hafner (2011) Econometric analysis of volatile art markets ISBA DP 2011-29, Computational Statistics and Data Analysis, forthcoming. Einmahl, J.H.J., Krajina, A. and J. Segers (2011) An M-estimator for tail dependence in arbitrary dimension, ISBA DP 2011-05 Franke, J., Fiecas, M., von Sachs, R. and J. Tadjuidje (2011). Shrinkage estimation for multivariate Hidden Markov mixing models. Mimeo. Gudendorf, G. and J. Segers (2011) Nonparametric estimation of multivariate extreme-value copulas, ISBA DP 2011-18 Kojadinovic, I., Segers, J. and J. Yan (2011) Large-sample tests of extreme-value dependence for multivariate copulas ISBA DP 2011-12 and The Canadian Journal of Statistics, 39, 97-111. 3.4.2. Liste des parutions (livres et/ou articles) Autin, F., Freyermuth, J.-M. and R. von Sachs (2011a), Ideal denoising within a family of tree-structured wavelet estimators - Electronic Journal of Statistics, 5, 829-855, 2011.

Basrak, B., Krizmanic, D. and J. Segers (2011), A functional limit theorem for partial sums of dependent random variables with infinite variance, The Annals of Probability, Forthcoming.

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Bauwens, L. and J.V.K. Rombouts (2011), On marginal likelihood computation in change-point models - Computational Statistics and Data Analysis, Forthcoming.

Bauwens, L., Hafner, C.M. and Laurent, S. (2012), Handbook of Volatility Models and Their Applications, Wiley, forthcoming. Bauwens, L., Hafner, C.M. and D. Pierret (2011), Multivariate volatility modeling of electricity futures, Journal of Applied Econometrics, forthcoming.

Eichler, M., Motta, G. and R. von Sachs (2011), Fitting dynamic factor models to non-stationary time series - Journal of Econometrics 2011, Special Issue on "Factor Structures for Panel and Multivariate Time Series Data", 163, 51-70, 2011.

Guillotte, S., Perron, F. and J. Segers (2011), Non-parametric Bayesian inference on bivariate extremes - Journal of the Royal Society. Series B, Statistical Methodology, 73, 3, 377-406, 2011.

Gudendorf, G. and J. Segers (2011), Nonparametric estimation of an extreme-value copula in arbitrary dimensions - Journal of Multivariate Analysis, 102, 37-47, 2011.

Hafner, C.M. and H. Manner (2011), Multivariate time series models for asset prices - Handbook of Computational Finance, Springer Verlag, Forthcoming. Hafner, C.M. and H. Manner (2012), Dynamic stochastic copula models: Estimation, inference and applications - Journal of Applied Econometrics, 27 (2), 269–295. Hafner, C.M. and O. Reznikova (2011), On the estimation of dynamic conditional correlation models - Computational Statistics and Data Analysis, Forthcoming. Hafner, C.M. and Shin-Huei Wang (2011), Estimating autocorrelations in the presence of deterministic trends - Journal of Time Series Econometrics, 3, 1–23. Kojadinovic, I., Segers, J. and Yan, J. (2011), Large-sample tests of extreme-value dependence for multivariate copulas, The Canadian Journal of Statistics, 39, 97-111. Manner, H. and O. Reznikova (2012), Time-varying copulas: a survey, Econometric Reviews, 31, 654-687.

Manner, H. and J. Segers (2011), Tails of correlation mixtures of elliptical copulas - Insurance: Mathematics and Economics, 48, 153-160, 2011.

Meinguet, T. (2011), Maxima of moving maxima of continuous functions, Extremes, DOI 10.1007/s10687-011-0136-8, forthcoming. Motta, G., Hafner, C. and R. von Sachs (2011), Locally stationary factor models: identification and nonparametric estimation, Econometric Theory, 27 (6), 1279-1319.

Roueff, F. and R. von Sachs (2011), Locally stationary long memory estimation - Stochastic Processes and their Applications, 121, 813-844, 2011.

Segers, J. (2011a), Comments on Inference in multivariate Archimedean copula models - Test, An Official Journal of the Spanish Society of Statistics and Operations Research, 19, 1, 2011.

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Segers, J. (2011b), Asymptotics of empirical copula processes under nonrestrictive smoothness assumptions, Bernoulli, forthcoming.

Van Dijk, D., Munandar, H., and C.M. Hafner (2011), The Euro-introduction and non-Euro currencies - Applied Financial Economics, 21, 95-116, 2011.

3.5. Visites principales en 2011 3.5.1.a. Visites principales Dimitris Korobilis, University of Strahclyde, United Kingdom February 16, 2011 “On adaptative shrinkage priors for forecasting with many predictors” Timothy J. Vogelsang, Michigan State University, USA March 9, 2011 “Integrated Modified OLS estimation and Fixed-b inference for cointegrating regressions” Piotr Fryzlewicz, London School of Economics (LSE), United Kingdom April 1, 2011 “Haar-Fisz methodology for interpretable estimation of large, sparse, time-varying volatility matrices” Olivier Wintenberger, Paris, France April 1, 2011 “Detecting multiple change points using Quasi Likelihood” Axel Bücher, Ruhr-University of Bochum, Germany October 21, 2011 “New estimators of the Pickands dependence function and a test for extreme-value dependence” Melanie Schienle, Humboldt-University of Berlin, Germany November 21, 2011 “Semiparametric Estimation with Generated Covariates” Paul Doukhan, University of Cergy-Pontoise, Member of the French Universitary Institute (IUF), France December 16, 2011 “Modeling integer valued time series”

3.5.1.b. Professeur /Chercheur visiteur Professeur Jeroen Rombouts, HEC Montréal, Québec : Jusqu'au 30/06/2011 au CORE Dimitris Korobilis, University of Strathclyde, Glasgow, United Kingdom Jusqu'au 31/08/2011, postdoctorant au CORE

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3.5.2. Missions effectuées Bauwens, Luc Mars 2011 - Colloque "Latest Developments in Financial Econometrics" “Change-point GARCH models” ECARES, ULB, Bruxelles, Belgique Avril 2011 Séminaire d'économie "CAW-DCC: A dynamic model for vast realized covariance matrices Université de Sassari, Italie Mai 2011 Interdisciplinary workshop on "Econometric and statistical modelling of multivariate time series’ "CAW-DCC: A dynamic model for vast realized covariance matrices" UCL, Louvain-la-Neuve, Belgique Octobre 2011 Basel III and Beyond: Regulating and Supervising Banks in the Post-Crisis Era Eltville, Allemagne Séminaire d’économétrie "CAW-DCC: A dynamic model for vast realized covariance matrices CREATES, Aarhus University, Danemark Conference on Measuring Risk, Bendheim Center for Finance. "CAW-DCC: A dynamic model for vast realized covariance matrices Princeton University, USA Novembre 2011 European Seminar on Bayesian Econometrics “Change-point GARCH models” Bruxelles, Belgique Dufays, Arnaud Mai 2011 - Interdisciplinary workshop on "Econometric and statistical modelling of multivariate time series" Présentation d'un poster "Change-point GARCH models and marginal likelihood computation using discrete differential evolution Monte Carlo" UCL, Louvain-la-Neuve, Belgique Septembre 2011

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- 10th OxMetrics User Conference "Change-Point Garch Models and marginal likelihood computation using discrete differential evolution Monte Carlo" Maastricht, Pays-Bas Novembre 2011 - European Seminar on Bayesian Econometrics (W11 & W12) Bruxelles, Belgique Décembre 2011 - Computational and Financial Econometrics London, United Kingdom Hafner, Christian Février 2011 - Conférence "Verein fuer Socialpolitik, Oekonometrischer Ausschuss" Schloss Rauischholzhausen, Allemagne Mars 2011 - Conférence "Extreme dependence in financial markets" Discussion of "Dynamic correlation or tail dependence hedging for portfolio selection'' by Elkamhi and Stefanova Erasmus University Rotterdam, Pays-Bas - Seminaire CREATES "Modelling multivariate volatility of electricity futures'' Aarhus University, Danemark Mai 2011 - Interdisciplinary workshop on "Econometric and statistical modelling of multivariate time series" "Macroeconomic news surprises and volatility spillover in the foreign exchange markets" UCL, Louvain-la-Neuve, Belgique Juin 2011 - Conférence "International symposium on forecasting multivariate modelling of electricity futures" Prague, République tchèque Septembre 2011 - Conférence "Statistische Woche, Deutsche Statistische Gesellschaft" Leipzig, Allemagne Décembre 2011 - Séminaire WIAS and Humboldt-Universitaet zu Berlin "Volatility of price indices for heterogenous goods" Berlin, Allemagne

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Pierret, Diane Mai 2011 - Interdisciplinary workshop on "Econometric and statistical modelling of multivariate time series" Présentation d'un poster "Multivariate volatility modeling of electricity futures" UCL, Louvain-la-Neuve, Belgique - AFI Finance workshop KUL, Louvain, Belgique Août 2011 - 65th European meeting of econometrics society (ESEM 2011) "Multivariate modeling of electricity futures" Oslo, Norvège Septembre 2011 - 10th OxMetrics User Conference "New risk measures in energy markets" Maastricht, Pays-Bas Octobre 2011 - Short course on Modelling heterogeneity in econometrics (Jerry A. Hausman) - Humboldt-Princeton Conference: Risk patterns in economics, statistics, finance and medicine Berlin, Allemagne - 19th Annual meeting of the Belgian statistical society Hasselt, Belgique Décembre 2011 Programme de "Visiting Scholar" à l'université de New York sous la direction du professeur Robert F. Engle du 28/12/2011au 30/06/2012, New York, USA Segers, Johan Janvier 2011 - Visite de recherche avec François Roueff, TELECOM ParisTech Paris, France Février 2011 - Kick-off meeting FWO-WOG "Stochastic modelling with applications in financial markets" "Extremes and dependence", Université de Gand, Belgique Avril 2011 - CIRM workshop "Dependence in probability and statistics" "The tail process of a regularly varying time series"

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Marseille - Luminy, France Mai 2011 - "International Symposium on Recent advances in statistics and probability" Université de Hasselt, Hasselt, Belgique - Interdisciplinary workshop on "Econometric and statistical modelling of multivariate time series" "Modelling extremes of multivariate time series via the tail process" UCL, Louvain-la-Neuve, Belgique Juin 2011 - CRM workshop "Copula models and dependence" "Studying extremal dependence via copulas" Université de Montréal, Montréal - Extreme value analysis, probabilistic and statistical models extreme Bayesian inference for bivariate extremes - EVA 2011" "Nonparametric Bayesian Inference on Bivariate Extremes" Université Lyon 1, Lyon, France Septembre 2011 - Workshop "New developments in econometrics and time series" "Multivariate extremes: Theory, models, and inference" ULB, Bruxelles, Belgique Novembre 2011 - Visite de recherche à Holger Rootzén et participation au jury de thèse de Dmitrii Zholud, Chalmers University of Technology "Extreme value analysis of huge datasets - Tail estimation methods in high-throughput screening and bioinformatics" Gothenburg, Suède - Visite de recherche à Nils Lid Hjort et participation au jury de thèse de Steffen Grønnenberg "Some applications of stochastic process techniques to statistics" Oslo University, Oslo, Norvège - Interuniversity Attraction Pole on Statistics Workshop 5 "Dependence and copulas" UCL, Louvain-la-Neuve, Belgique Décembre 2011 - Vidéoconférence par téléphone et via l'internet organisé par le working group Statistics of Extremes de l'institut SAMSI aux Etats-Unis "An M-estimator for tail dependence in arbitrary dimensions" - Visite de recherche à Véronique Maume-Deschamps et participation au jury de thèse d'Elena di Bernardino Université de Lyon 1, Lyon, France

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Koch, Daniel Mai 2011 - Interdisciplinary workshop on "Econometric and statistical modelling of multivariate time series” UCL, Louvain-la-Neuve, Belgique Octobre 2011 - 19th Annual meeting of the Belgian statistical society "High-dimensional portfolio optimization using wavelet thresholding" Hasselt, Belgique Décembre 2011 - 4th International conference of the ERCIM WG on computing "High-dimensional portfolio optimization using wavelet thresholding" Londres, Grande-Bretagne Van Bellegem, Sébastien Décembre 2010 - Janvier 2011 - Séjour de recherche University of Pontificale, Chile - Séjour de recherche University of Santiago de Chile, Chile Mars 2011 - Recherche sur les modèles à facteurs endogènes Séminaire Santiago de Chile, Chile Mai 2011 - Interdisciplinary workshop on "Econometric and statistical modelling of multivariate time series’ UCL, Louvain-la-Neuve, Belgique von Sachs, Rainer Mai 2011 - Interdisciplinary workshop on "Econometric and statistical modelling of multivariate time series’ UCL, Louvain-la-Neuve, Belgique Juillet 2011 - Séjour de recherche scientifique avec le Professeur Piotr Fryzlewicz London School of Economics, Londres, Grande-Bretagne

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Août 2011 - Séjour de recherche scientifique avec le Professeur Jürgen Franke Kaiserslautern, Allemagne Décembre 2011 - Séjour de recherche scientifique avec le Professeur François Roueff Paris Tech, Paris, France Freyermuth, Jean-Marc Avril 2011 - Séjour de recherche scientifique avec Florin Autin Université de Marseille, France Mai 2011 - Interdisciplinary workshop on "Econometric and statistical modelling of multivariate time series” UCL, Louvain-la-Neuve, Belgique Gudendorf, Gordon Mai 2011 - Interdisciplinary workshop on "Econometric and statistical modelling of multivariate time series’ UCL, Louvain-la-Neuve, Belgique Octobre 2011 - 19th Annual meeting of the Belgian statistical society "Nonparametric estimation of multivariate extreme value copulas" Hasselt, Belgique

3.5.3. Organisation d’un colloque interdisciplinaire les 25, 26 et 27 mai 2011 "Econometric and statistical modelling of multivariate time series" Ce colloque interdisciplinaire à la frontière entre l’économétrie et la statistique a traité de questions substantielles dans le domaine de la modélisation des séries chronologiques multivariées. Il fut organisé par l’équipe des promoteurs du projet ARC 07-12/002 portant sur la même problématique scientifique. Les sujets abordés lors de ce colloque étaient, en particulier, les modèles multivariés de volatilité, les données de hautes fréquences, la modélisation des valeurs extrêmes, la réduction de dimension et les modèles à facteurs, les modèles à paramètres évolutifs dans le temps et les modèles de changements structurels, ainsi que la prévision des séries chronologiques. Une centaine de chercheurs locaux et internationaux ont suivi pendant ces trois jours 14 exposés oraux suivis dans la grande majorité des cas d’une discussion stimulante entre conférenciers et audience. En autre, deux sessions de posters ont été organisées pour permettre à une quarantaine de jeunes chercheurs de présenter leurs travaux d’avancement de

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thèse ou leurs résultats de recherche postdoctorale. Ces sessions ont été suivies très activement par nos conférenciers invités de sorte que les jeunes auteurs des posters ont profité de l’intérêt et des remarques appréciés de leurs collègues seniors. La présence du Professeur Robert Engle de l’Université de New York, prix Nobel de sciences économiques en 2003, a évidemment contribué au grand succès de ce colloque. La qualité de son exposé en séance plénière, enregistré et mis en ligne sur le site de l’UCL, sa disponibilité à mener des discussions fortement enrichissantes et son intérêt pour la recherche dans tous les domaines du colloque ont reçu la gratitude et la satisfaction générale. Ainsi, les organisateurs du colloque peuvent se féliciter d’avoir atteint le double objectif qu’ils s’étaient fixé d'avoir stimuler la discussion scientifique d'une part entre visiteurs internationaux (souvent experts mondiaux dans leur domaine) et promoteurs du projet ARC local sollicitant ainsi un regard externe sur leurs travaux en cours et d’autre part entre des chercheurs expérimentés et jeune public doctoral et postdoctoral. On pourrait résumer cet événement scientifique comme un grand succès pour la visibilité internationale de l’Institut IMMAQ qui héberge les chercheurs du projet ARC et de toute l’institution Université catholique de Louvain. Comité scientifique Luc Bauwens (UCL) Christian Hafner (UCL) Rainer von Sachs (UCL) Johan Segers (UCL) Sébastien Van Bellegem (UCL) David Veredas (ULB) Programme 25 mai 2011

• Ouverture : Vincent Yzerbyt, prorecteur à la recherche, UCL • Session 1 (président : David Veredas, ULB) • Timo Teräsvirta (Aarhus University & CREATES, Denmark)

"Nonlinear forecasting of macroeconomic variables using automated model selection techniques"

• Luc Bauwens (UCL, CORE) "CAW-DCC: a dynamic model for vast realized covariance matrices"

• Session posters (1) • Session 2 (président : François Roueff, Telecom ParisTech, France) • Jun Yu (Singapore Management University, Singapore)

"Bias in Estimating Multivariate and Univariate Diffusions" • Dennis Kristensen (Columbia University, USA)

"Estimation of Diffusion Models with Time-varying Parameters" • Réception

26 mai 2011

• Keynote Session (Président : Luc Bauwens, UCL, CORE) • Keynote lecture: Robert F. Engle (New York University Stern School of Business,

USA) "Volatility, Correlation and Tails for Systemic Risk Measurement"

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• Session posters (2) • Session 3 (président : Manfred Deistler, Vienna University of Technology, Austria) • Qiwei Yao (London School of Economics, United Kingdom)

"Factor modelling for high-dimensional time series: a dimension-reduction approach" • Christian Gouriéroux (University of Toronto, Canada & CREST, France)

"Correlated Risks vc Contagion in Stochastic Transition Models" • Session 4 (président : Franz Palm, Maastricht University, The Netherlands) • Johan Segers (UCL, ISBA, Belgium)

"Modelling extremes of multivariate time series via the tail process" • Matteo Barigozzi (London School of Economics and Political Science, United

Kingdom) "Which models to match?"

• Dimitris Korobilis (UCL, CORE) "Assessing the transmission of monetary policy shocks using dynamic"

• Conference dinner Aula Magna, Louvain-la-Neuve 27 mai 2011

• Session 5 (président : Piotr Fryzlewicz, London School of Economics and Political Science, United Kingdom)

• Christian Hafner (UCL, ISBA) • "Macroeconomic News Surprises and Volatility Spillover in the Foreign Exchange

Markets" • Jeroen Rombouts (HEC Montreal, Canada)

"Marginal Likelihood for Markov-Switching and Change-Point Garch Models" • Session 6 (président : Jürgen Franke, University of Kaiserslautern, Germany) • Marc Hallin (ULB, ECARES)

"Quantiles, Time Series, and Spectral Analysis" • Richard A. Davis (Columbia University, USA)

"Noncausal Vector AR Processes with Application to Financial Time Series” • Closing lunch

Site web de la conference: http://www.uclouvain.be/en-332033.html 3.6. Matériel « exceptionnel » réceptionné en 2011 Aucun matériel de ce type n’a été réceptionné pendant l’année écoulée. 3.7. Prévisions d’activités pour 2012 Séminaires February 6, 2012 Jean-Marie Dufour, McGill University, Quebec "Exogeneity tests, weak identification and IV estimation:Is the cure worse than the illness? February 27, 2012

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Abdelaati Daouia, ISBA, UCL, Belgium "On Projection-Type Estimators of Multivariate Isotonic Functions" March 26, 2012 Dennis Kristensen, University College of London, United Kingdom "Optimal Sampling and Bandwidth Selection for Kernel Estimators of Diffusion Processes" (joint with Shin Kanaya, CREATES) April 16, 2012 Martin Wagner, Institute for Advanced Studies, Vienna, Austria "On the econometric analysis of the environmental Kuznets curve"

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ANNEXE A

PERSONNEL A CHARGE DU PROGRAMME Cette annexe reprend

- un tableau synthétique décrivant les membres du personnel à charge de la convention ARC

- les fiches de renseignements dûment complétées par le Service du Personnel de

l’UCL.

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ANNEXE IV.a PERSONNEL A CHARGE DE L’ACTION DE RECHERCHE CONCERTEE CONVENTION N° : .................. 07/12-002………..…………….. ANNEE CIVILE : .... 2011......... PROMOTEURS (PORTE-PAROLE ET CO-PROMOTEUR(S)) : R. von Sachs (promoteur porte-parole du projet), L. Bauwens, C. Hafner, J. Segers

NOM, PRENOM

TYPE*

E.T.P.

Période d’occupation

Freyermuth Jean-Marc Tanga Monique Gudendorf Gordon Dufays Arnaud Pierret Diane

Doctorant boursier Administratif Doctorant boursier Doctorant boursier Doctorante boursière

1 50% 30 % 50% 1 1 1

1/10/2007 -30/09/2011 25/10/2007 - 29/02/2008 01/03/2008 - 31/ 03/2009 01/10/2009 - 30/09/2012 10/09/2010 - 09/09/2012 15/09/2009 - 14/09/2011 15/09/2010 – 13/03/2012

* A PRECISER SELON LE CAS : Scientifique (c-à-d doctorant boursier, doctorant contractuel, post-doctorant boursier, post-doctorant contractuel, senior, autres à préciser), technique ou administratif.

33

34

35

36

37

38

ANNEXE B PERSONNEL NON A CHARGE MAIS TRAVAILLANT SUR LES THEMES DE L’ARC Cette annexe reprend un tableau synthétique décrivant les membres du personnel non à charge de la convention ARC mais travaillant sur des thèmes proches de ceux de l’ARC

ANNEXE IV.b PERSONNEL NON A CHARGE DE L’ACTION DE RECHERCHE CONCERTEE

CONVENTION N°: 07/12-002 ANNEE CIVILE : 2011

PROMOTEURS (PORTE-PAROLE ET CO-PROMOTEUR(S)) :

R. von Sachs (promoteur porte-parole du projet), L. Bauwens, C. Hafner, J. Segers

NOM, PRENOM TYPE* Source de financement + période d’occupation

% occupation sur l’ARC

Période d’occupation sur l’ARC

BAUWENS, Luc HAFNER, Christian von SACHS, Rainer SAMKHARADZE Besik SEGERS Johan KOCH Daniel VAN BELLEGEM Sébastien BOCART Fabian

Promoteur Promoteur Promoteur Doctorant Promoteur Doctorant Professeur Assistant

UCL-CORE UCL-ISBA UCL- ISBA UCL-CORE UCL-ISBA UCL-ISBA UCL-CORE UCL-ISBA

30% 30% 30% 50% 30% 75% 30% 50%

01/01/2011-31/12/2011 01/01/2011-31/12/2011 01/01/2011-31/12/2011 01/01/2011-31/12/2011 01/01/2011-31/12/2011 01/01/2011-31/12/2011 01/01/2011-31/12/2011 01/01/2011-31/12/2011

* A PRECISER SELON LE CAS : Scientifique (c-à-d doctorant boursier, doctorant contractuel, post-doctorant boursier, post-doctorant contractuel, senior, autres à préciser), technique ou administratif.