Relevant states and memory in Markov chain bootstrapping and simulation

Markov chain theory is proving to be a powerful approach to bootstrap and simulate highly nonlinear time series. In this work, we provide a method to estimate the memory of a Markov chain (i.e. its order) and to identify its relevant states. In particular, the choice of memory lags and the aggregation of irrelevant states are obtained by looking for regularities in the transition probabilities. Our approach is based on an optimization model. More specifically, we consider two competing objectives that a researcher will in general pursue when dealing with bootstrapping and simulation: preserving the “structural” similarity between the original and the resampled series, and assuring a controlled diversification of the latter. A discussion based on information theory is developed to define the desirable properties for such optimal criteria. Two numerical tests are developed to verify the effectiveness of the proposed method

Approximating Markov Chains for Bootstrapping and Simulation

In this work we develop a bootstrap method based on the theory of Markov chains. The method moves from the two competing objectives that a researcher pursues when performing a bootstrap procedure: (i) to preserve the structural similarity -in statistical sense- between the original and the bootstrapped sample; (ii) to assure a diversification of the latter with respect to the former. The original sample is assumed to be driven by a Markov chain. The approach we follow is to implement an optimization problem to estimate the memory of a Markov chain (i.e. its order) and to identify its relevant states. The basic ingredients of the model are the transition probabilities, whose distance is measured through a suitably defined functional. We apply the method to the series of electricity prices in Spain. A comparison with the Variable Length Markov Chain bootstrap, which is a well established bootstrap method, shows the superiority of our proposal in reproducing the dependence among data

A Tabu Search Heuristic Procedure in Markov Chain Bootstrapping

Markov chain theory is proving to be a powerful approach to bootstrap nite states processes, especially where time dependence is non linear. In this work we extend such approach to bootstrap discrete time continuous-valued processes. To this purpose we solve a minimization problem to partition the state space of a continuous-valued process into a nite number of intervals or unions of intervals (i.e. its states) and identify the time lags which provide \memory" to the process. A distance is used as objective function to stimulate the clustering of the states having similar transition probabilities. The problem of the exploding number of alternative partitions in the solution space (which grows with the number of states and the order of the Markov chain) is addressed through a Tabu Search algorithm. The method is applied to bootstrap the series of the German and Spanish electricity prices. The analysis of the results conrms the good consistency properties of the method we propose

A mixed integer linear program to compress transition probability matrices in Markov chain bootstrapping

Bootstrapping time series is one of the most acknowledged tools to study the statistical properties of an evolutive phenomenon. An important class of bootstrapping methods is based on the assumption that the sampled phenomenon evolves according to a Markov chain. This assumption does not apply when the process takes values in a continuous set, as it frequently happens with time series related to economic and financial phenomena. In this paper we apply the Markov chain theory for bootstrapping continuous-valued processes, starting from a suitable discretization of the support that provides the state space of a Markov chain of order k≥1. Even for small k, the number of rows of the transition probability matrix is generally too large and, in many practical cases, it may incorporate much more information than it is really required to replicate the phenomenon satisfactorily. The paper aims to study the problem of compressing the transition probability matrix while preserving the “law” characterising the process that generates the observed time series, in order to obtain bootstrapped series that maintain the typical features of the observed time series. For this purpose, we formulate a partitioning problem of the set of rows of such a matrix and propose a mixed integer linear program specifically tailored for this particular problem. We also provide an empirical analysis by applying our model to the time series of Spanish and German electricity prices, and we show that, in these medium size real-life instances, bootstrapped time series reproduce the typical features of the ones under observation. This is a post-peer-review, pre-copyedit version of an article published in Annals of Operations Research volume. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10479-016-2181-

The Strategic Exploitation of Limited Information and Opportunity in Networked Markets

This paper studies the effect of constraining interactions within a market. A model is analysed in which boundedly rational agents trade with and gather information from their neighbours within a trade network. It is demonstrated that a trader’s ability to profit and to identify the equilibrium price is positively correlated with its degree of connectivity within the market. Where traders differ in their number of potential trading partners, well-connected traders are found to benefit from aggressive trading behaviour.Where information propagation is constrained by the topology of the trade network, connectedness affects the nature of the strategies employed

Remarks on 2+1 Self-dual Chern-Simons Gravity

We study 2+1 Chern-Simons gravity at the classical action level. In particular we rederive the linear combinations of the ``standard'' and ``exotic'' Einstein actions, from the (anti) self-duality of the ``internal'' Lorentzian indices. The relation to a genuine four-dimensional (anti)self-dual topological theory greatly facilitates the analysis and its relation to hyperbolic three-dimensional geometry. Finally a non-abelian vector field ``dual'' action is also obtained.Comment: 16+1 pages, LaTeX file, no figures, clarifications and comments added, typos corrected and one reference adde

Sphingosine-1 phosphate induces cAMP/PKA-independent phosphorylation of the cAMP response element-binding protein (CREB) in granulosa cells

Background and aims: Sphingosine-1 phosphate (S1P) is a lysosphingolipid present in the ovarian follicular fluid. The role of the lysosphingolipid in gonads of the female is widely unclear. At nanomolar concentrations, S1P binds and activates five specific G protein-coupled receptors (GPCRs), known as S1P1-5, modulating different signaling pathways. S1P1 and S1P3 are highly expressed in human primary granulosa lutein cells (hGLC), as well as in the immortalized human primary granulosa cell line hGL5. In this study, we evaluated the signaling cascade activated by S1P and its synthetic analogues in hGLC and hGL5 cells, exploring the biological relevance of S1PR-stimulation in this context. METHODS AND RESULTS. hGLC and hGL5 cells were treated with a fixed dose (0.1 \u3bcM) of S1P, or by S1P1- and S1P3-specific agonists SEW2871 and CYM5541. In granulosa cells, S1P and, at a lesser extent, SEW2871 and CYM5541, potently induced CREB phosphorylation. No cAMP production was detected and pCREB activation occurred even in the presence of the PKA inhibitor H-89. Moreover, S1P-dependent CREB phosphorylation was dampened by the mitogen-activate protein kinase (MEK) inhibitor U0126 and by the L-type Ca2+ channel blocker verapamil. The complete inhibition of CREB phosphorylation occurred by blocking either S1P2 or S1P3 with the specific receptor antagonists JTE-013 and TY52156, or under PLC/PI3K depletion. S1P-dependent CREB phosphorylation induced FOXO1 and the EGF-like epiregulin-encoding gene (EREG), confirming the exclusive role of gonadotropins and interleukins in this process, but did not affect steroidogenesis. However, S1P or agonists did not modulate granulosa cell viability and proliferation in our conditions. Conclusions: This study demonstrates for the first time that S1P may induce a cAMP-independent activation of pCREB in granulosa cells, although this is not sufficient to induce intracellular steroidogenic signals and progesterone synthesis. S1P-induced FOXO1 and EREG gene expression suggests that the activation of S1P\u2013S1PR axis may cooperate with gonadotropins in modulating follicle development