Portfolio optimization with mixture vector autoregressive models

Obtaining reliable estimates of conditional covariance matrices is an important task of heteroskedastic multivariate time series. In portfolio optimization and financial risk management, it is crucial to provide measures of uncertainty and risk as accurately as possible. We propose using mixture vector autoregressive (MVAR) models for portfolio optimization. Combining a mixture of distributions that depend on the recent history of the process, MVAR models can accommodate asymmetry, multimodality, heteroskedasticity and cross-correlation in multivariate time series data. For mixtures of Normal components, we exploit a property of the multivariate Normal distribution to obtain explicit formulas of conditional predictive distributions of returns on a portfolio of assets. After showing how the method works, we perform a comparison with other relevant multivariate time series models on real stock return data.Comment: 19 pages, 9 figures, 2 table

Sharp measure contraction property for generalized H-type Carnot groups

We prove that H-type Carnot groups of rank $k$ and dimension $n$ satisfy the $\mathrm{MCP}(K,N)$ if and only if $K\leq 0$ and $N \geq k+3(n-k)$. The latter integer coincides with the geodesic dimension of the Carnot group. The same result holds true for the larger class of generalized H-type Carnot groups introduced in this paper, and for which we compute explicitly the optimal synthesis. This constitutes the largest class of Carnot groups for which the curvature exponent coincides with the geodesic dimension. We stress that generalized H-type Carnot groups have step 2, include all corank 1 groups and, in general, admit abnormal minimizing curves. As a corollary, we prove the absolute continuity of the Wasserstein geodesics for the quadratic cost on all generalized H-type Carnot groups.Comment: 18 pages. This article extends the results of arXiv:1510.05960. v2: revised and improved version. v3: final version, to appear in Commun. Contemp. Mat

Flavored tetraquark spectroscopy

The recent confirmation of the charged charmonium like resonance Z(4430) by the LHCb experiment strongly suggests the existence of QCD multi quark bound states. Some preliminary results about hypothetical flavored tetraquark mesons are reported. Such states are particularly amenable to Lattice QCD studies as their interpolating operators do not overlap with those of ordinary hidden-charm mesons

Bayesian analysis of mixture autoregressive models covering the complete parameter space

Mixture autoregressive (MAR) models provide a flexible way to model time series with predictive distributions which depend on the recent history of the process and are able to accommodate asymmetry and multimodality. Bayesian inference for such models offers the additional advantage of incorporating the uncertainty in the estimated models into the predictions. We introduce a new way of sampling from the posterior distribution of the parameters of MAR models which allows for covering the complete parameter space of the models, unlike previous approaches. We also propose a relabelling algorithm to deal a posteriori with label switching. We apply our new method to simulated and real datasets, discuss the accuracy and performance of our new method, as well as its advantages over previous studies. The idea of density forecasting using MCMC output is also introduced.Comment: 27 pages, 10 figures, 4 table

Constraining the fraction of binary black holes formed in isolation and young star clusters with gravitational-wave data

Ten binary black-hole mergers have already been detected during the first two observing runs of advanced LIGO and Virgo, and many more are expected to be observed in the near future. This opens the possibility for gravitational-wave astronomy to better constrain the properties of black hole binaries, not only as single sources, but as a whole astrophysical population. In this paper, we address the problem of using gravitational-wave measurements to estimate the proportion of merging black holes produced either via isolated binaries or binaries evolving in young star clusters. To this end, we use a Bayesian hierarchical modeling approach applied to catalogs of merging binary black holes generated using state-of-the-art population synthesis and N-body codes. In particular, we show that, although current advanced LIGO/Virgo observations only mildly constrain the mixing fraction $f \in [0,1]$ between the two formation channels, we expect to narrow down the fractional errors on $f$ to $10-20\%$ after a few hundreds of detections.Comment: 17 pages, 4 figure