We consider reasoning and minimization in systems of polynomial ordinary differential equations (ode's). The ring of multivariate polynomials is employed as a syntax for denoting system behaviours. We endow polynomials with a transition system structure based on the concept of Lie derivative, thus inducing a notion of L-bisimulation. Two states (variables) are proven \lbisim-bisimilar if and only if they correspond to the same solution in the ode's system. We then characterize L-bisimilarity algebraically, in terms of certain ideals in the polynomial ring that are invariant under Lie-derivation. This characterization allows us to develop a complete algorithm, based on building an ascending chain of ideals, for computing the largest L-bisimulation containing all valid identities that are instances of a user-specified template. A specific largest L-bisimulation can be used to build a reduced system of ode's, equivalent to the original one, but minimal among all those obtainable by linear aggregation of the original equations.
We discuss several multivariate extensions of the Multiplicative Error Model by Engle (2002) to take into account dynamic interdependence and contemporaneously correlated innovations (vector MEM or vMEM). We suggest copula functions to link Gamma marginals of the innovations, in a specification where past values and conditional expectations of the variables can be simultaneously estimated. Results with realized volatility, volumes and number of trades of the JNJ stock show that significantly superior realized volatility forecasts are delivered with a fully interdependent vMEM relative to a single equation. Alternatives involving log–Normal or semiparametric formulations produce substantially equivalent results.
This paper posits that the municipality level offers important insights into the study of temporal and spatial patterns of family change. We focus on the diffusion of one-parent families in Italy: variation in the structure of co-resident domestic groups is a crucial indicator of changing diversity in family patterns. We apply a hierarchical Bayesian spatio-temporal model to the data of the last three Italian Population Censuses, at the municipality level. Our results show substantial sub-regional and sub-provincial heterogeneities in the spatial organization of family systems. These patterns might have gone undetected if larger territorial units of analysis had been considered.
Public support to start-ups often has the dual ambition of fostering self-employment of disadvantaged individuals while nurturing entrepreneurship. In this paper we evaluate a female and youth start-up program recently implemented in Tuscany (Italy), which provides public guarantees and subsidized interest rates to new firms. Under the assumption of strong ignorability of the assignment mechanism, we use a propensity score matching approach to draw inference on causal effects of the program on firms’ survival and job creation. Results suggest that public support in this area may have rather ambiguous effects. It helps females and young people escape unemployment or inactivity, and may lead to further job creation. Unfortunately, all this occurs at the price of committing public resources towards entrepreneurial projects that hardly gain efficiency over time.
Volatility in financial markets is characterized by alternating persistent turmoil and quiet periods, but also by a slowly-varying average level. This slow moving component keeps open the question of whether some of its features are better represented as abrupt or smooth changes between local averages of volatility. We provide a new class of models with a set of parameters subject to abrupt changes in regime (Markov Switching -- MS) and another set subject to smooth transition (ST) changes. These models capture the possibility that regimes may overlap with one another (fuzzy). The empirical application is carried out on the volatility of four US indices. It shows that the flexibility of the new model allows for a better overall performance over either MS or ST, and provides a Local Average Volatility measure as a parametric estimation of the low frequency component.
Ultimo aggiornamento 29 agosto 2017 .