**25-28 June 2019****Casa della Gioventùvia Rio Bianco, 1239042 Brixen-Bressanone, Italy**

The Third YUIMA Conference is supported by Japan Science and Technology Agency CREST JPMJCR14D7; and Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research No. 17H01702 (Scientific Research).

**Invited Speakers**

Krzysztof Bartoszek (Linköping University)

Emmanuele Guidotti (University of Neuchâtel)

Stefano Iacus (University of Milan)

Francesco Iafrate (University of Rome “La Sapienza”)* *Yuta Koike (University of Tokyo)

Pietro Lio’ (University of Cambridge)

Hiroki Masuda (Kyushu University)

Lorenzo Mercuri (University of Milan)

Ioane Muni Toke (Centrale Supélec)

Nakahiro Yoshida (University of Tokyo)

##### Abstract of talks

**Krzysztof Bartoszek (Linköping University)**

*YUIMA for simulating traits and phylogenetics in the pcmabc R package*

The field of phylogenetic comparative methods deals with traits evolving on the between-species level. The suite of traits follows some stochastic process along the branches of the tree and, in most modelling setups, after speciation the daughter lineages evolve independently. Usually (but there are some exceptions) the trait’s transition density has to be parametrically known, is assumed Gaussian (or discrete) and evolution is conditional on the phylogeny. The pcmabc (Bartoszek and Lio’, 2019) R (R, 2018) package drops the latter assumptions. It suffices that one is able to provide a function to simulate the trait along a time interval, conditional on some ancestral value. There is no restriction on whether the trait should be continuous or discrete or a mix. Furthermore, the probability to speciate is allowed to depend on the trait’s value. Hence, the tree is simulated with the help of a rejection sampling algorithm for the Inhomogeneous Poisson process (Proposition p. 32, Ross 2006). Any simulation function that follows specific input and output rules can be provided by the user, however special support is given for simulation through the YUIMA R package (Brouste et. al., 2014). In the talk we will give special attention to the interface between pcmabc and YUIMA.

K. Bartoszek, P. Lio’ (2019). Modelling trait dependent speciation with Approximate Bayesian Computation. Acta Phys. Pol. B Proc. Suppl., 12(1), 25-47.

A. Brouste, M. Fukasawa, H. Hino, S. M. Iacus, K. Kamatani, Y. Koike, H. Masuda, R. Nomura, T. Ogihara, Y. Shimuzu, M. Uchida, N. Yoshida (2014). The YUIMA Project: A Computational Framework for Simulation and Inference of Stochastic Differential Equations. J. Stat. Softw., 57(4), 1-51.

R Core Team (2018). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.

S. M. Ross. Simulation. Elsevier AP. 2006.

**Emmanuele Guidotti (University of Neuchâtel)***Towards Coding of the Asymptotic Expansion Formula in YUIMA*

Based on the Malliavin-Watanabe theory, Yoshida presented a general asymptotic expansion formula designed to facilitate implementation.

The aim of this presentation is to show the current advances in the implementation of Asymptotic Expansion in YUIMA, open source academic project aimed at developing a complete environment for estimation and simulation of Stochastic Differential Equations and other Stochastic Processes via the R package called yuima and its Graphical User Interface yuimaGUI. The implementation of the asymptotic expansion formula would allow the user to efficiently compute expected values of multidimensional processes with virtually any degree of accuracy.

**Stefano Iacus (University of Milan)***On Regularized Estimation for Stochastic Differential Equations*

In this talk we will review recent results on regularization methods for the parametric estimation for high-dimensional dynamical systems with small noise and also for high- dimensional ergodic diffusions with discrete observations. Regularized estimation is at the same time a dimensionality reduction technique and model selection tool as well as an efficient estimation method especially in the case of high-dimensional systems which admit a sparse representation. Indeed, in such situation, variable selection becomes particularly important when it comes to correctly identify significant predictors that will improve the forecasting performance of the fitted model. In our talk we will consider regularized estimation from discrete observations of the multi-dimensional ergodic diffusion process with adaptive penalties. Numerical analysis will also be presented through the Yuima R package. We will later extend these analyses to the more general case of Adaptive Elastic Net estimation, which generalizes the LASSO method to a least square estimation method with both L1 and L2 penalties in the same objective function. We will show the advantages of this approach in the case when the dimension of the parameter space diverges with the sample size. This is an on-going joint work with A. De Gregorio and N. Yoshida.

**Francesco Iafrate (University of Rome “La Sapienza”)***Adaptive L^q penalized estimation for diffusion processes in Yuima package*

Penalized estimation methods have recently gained popularity in the field of inference for stochastic processes. We present some generalizations of known results for diffusion processes as well as an implementation of these estimation techniques in the framework of the Yuima package. We also discuss some criteria for the selection of the tuning parameters as an alternative to standard cross-validation techniques for non i.i.d. data.

**Yuta Koike (University of Tokyo)***High-dimensional covariance estimation in YUIMA package*

In the past decade, there has been much progress in estimating high-dimensional covariance and precision matrices of a discretely observed diffusion process. In this talk, we discuss how to implement methods developed there in the yuima package. We also demonstrate recent progress in inference for those objects.

**Pietro Lio’ (University of Cambridge)***Molecular data integration, Evolutionary trajectories and diseases*

I will describe two approaches that combine machine learning and bioinformatics and also integrate different molecular information. First, I will use an Ornstein–Uhlenbeck phylogenetic approach to identify disease associated genes by integrating the gene expression and DNA methylation data. On the basis of the identified genes, I will explore the correlations among the inflammation related diseases. The method results in identifying the way member of gene families interact. Then I will construct a multiplex

machine learning model, which combines several Gaussian mixture hidden Markov model layers into a single multiplex model to integrate different types of molecular data. Finally I will discuss interesting bioinformatics problems that could require stochastic approaches.

**Hiroki Masuda (Kyushu University)**

*On Lévy driven models in YUIMA*

Lévy driven models constitute fundamental tools for analyzing time-varying non-Gaussian phenomena. YUIMA package allows us to generate high-frequency sample from a variety of Lévy driven models, and also to estimate them through some internal particular functions. In this talk, we will demonstrate what YUIMA currently can do about some specific Lévy driven models, along with briefly reviewing the associated background theory. Also mentioned is some recent results on inference of locally stable regression models, to be implemented into YUIMA.

**Lorenzo Mercuri (University of Milan)***COGARCH(p,q) model: simulation, estimation and an application in portfolio selection*

In this talk we review the algorithms for simulation and estimation of a COGARCH(p,q) model in the YUIMA package.

We discuss also the COGARCH.rm package where we propose a multivariate Independent Component COGARCH(p,q) model for financial time series. This new package allows to estimate and simulate scenarios of an ICA-COGARCH model. The model is able to capture heteroskedasticity and dependence in high-frequency not equally spaced observed financial time series.

We apply the model in scenario generation at any time-horizon and construct a decision-tree in order to determine optimal portfolio weights obtained as a solution of a static maximization problem. The objective function is a linear combination of expected terminal wealth and a specific risk measure.

**Ioane Muni Toke (Centrale Supélec)***Point processes modelling of limit order book events*

Limit order books are the core structure of modern financial exchanges, aggregating buy and sell orders of market participants. We introduce a Cox-type model for relative intensities of orders flows in a limit order book. The model assumes that all intensities share a common baseline intensity, which may for example represent the global market activity. Parameters can be estimated by quasi-likelihood maximization, without any interference from the baseline intensity. We recall some of these results and start to investigate the use of such models as a prediction tool. In theoretical context with no latency or computational cost, we show that the model may improve Hawkes-based predictions in the prediction of e.g., the next trade signs or the next price movement trade-through.

**Nakahiro Yoshida (University of Tokyo and Japan Science and Technology Agency CREST)***Adaptive and non-adaptive estimation of degenerate diffusion processes*

We estimate unknown parameters by using long-term high frequency data of a degenerate diffusion process. The convergence rate of the estimator for the parameter in the degenerate component becomes faster than other parameters in the non-degenerate component. Asymptotic normality of the estimators are obtained. We discuss an adaptive method based on the existing estimators for the non-degenerate component, and a non-adaptive method without initial estimators. Degenerate diffusions are used in various applications. An extension of the YUIMA qmle is now required.