Empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset. The paper presents a rigorous analysis for the case when the stationary stochastic volatility model is constructed in terms of a fractional Ornstein Uhlenbeck process to have such correlations. It is shown how the associated implied volatility has a term structure that is a f...

In this manuscript, we show how higher-order graphical models can be applied to study the controllability of networked systems with dynamic topologies. Studying empirical data on temporal networks, we specifically show that the order correlations in the activation sequence of links can both increase or reduce the time needed to achieve full controllability. We then demonstrate how spectral prop...

Taking countries of the Organization for Economic Co-operation and Development (OECD), this paper analyzes factors affecting their software piracy rate (SPR) by taking into account several economic and technological variables. The empirical results show that per capita GDP (PerGDP), inflation, consumer prices (ICP), unemployment rate (UR), and high-technology exports (HTE) have positive correla...

To study the statistical structure of crosscorrelations in empirical data, we generalize random matrix theory and propose a new method of cross-correlation analysis, known as autoregressive random matrix theory (ARRMT). ARRMT takes into account the influence of auto-correlations in the study of cross-correlations in multiple time series. We first analytically and numerically determine how auto-...

Soil thermal conductivity is significantly influenced by saturation and dry density. In this paper, a family of empirical correlations are presented which relate soil thermal conductivity to saturation for five soil types, namely, gravel, sand, silt, clay and peat, in both the frozen and unfrozen states. These correlations were developed from a soil thermal conductivity database which was const...

We analyze the European transition economics and show that many time series of major indices exhibit (i) power-law correlations in their values, (ii) power-law correlations in their magnitudes and (iii) an asymmetric probability distribution. Applying the phase randomization procedure to these time series, we show that magnitude correlations completely vanish. We propose a stochastic model that...

This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general enough to include cases in which no minimum exists, as occurs typically, for instance, with standard boosting algorithms. Concretely, we first show that any...

Empirical evidence shows that entrepreneurs hold a large fraction of wealth, have higher saving rates than workers, and face substantial uninsurable entrepreneurial and investment risks. This paper constructs a heterogeneous-agent general equilibrium model with uninsurable entrepreneurial risk and capital-market imperfections to explore the implications of uninsurable entrepreneurial risk for w...

Let (X ,μ) be a probability space, set X to be distributed according to μ and put Y to be an unknown target random variable. In the usual setup in learning theory, one observes N independent couples (Xi, Yi)Ni=1 in X × R, distributed according to the joint distribution of X and Y . The goal is to construct a real-valued function f which is a good guess/prediction of Y . A standard way of measur...