Related papers: Bridging the ARCH model for finance and nonextensi…
We propose a Monte-Carlo-based method for reconstructing sparse signals in the formulation of sparse linear regression in a high-dimensional setting. The basic idea of this algorithm is to explicitly select variables or covariates to…
The framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems. The non-extensive statistical mechanics is usually introduced in a formal way, using the maximization of entropy. In…
The minimum mean square error of the estimation of a non Gaussian signal where observed from an additive white Gaussian noise channel's output, is analyzed. First, a quite general time-continuous channel model is assumed for which the…
SVR-GARCH model tends to "backward eavesdrop" when forecasting the financial time series volatility in which case it tends to simply produce the prediction by deviating the previous volatility. Though the SVR-GARCH model has achieved good…
Stochastic variational inference algorithms are derived for fitting various heteroskedastic time series models. We examine Gaussian, t, and skew-t response GARCH models and fit these using Gaussian variational approximating densities. We…
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…
Stylized facts of empirical assets log-returns $Z$ include the existence of (semi) heavy tailed distributions $f_Z(z)$ and a non-linear spectrum of Hurst exponents $\tau(\beta)$. Empirical data considered are daily prices of 10 large…
Using Gretl, I apply ARMA, Vector ARMA, VAR, state-space model with a Kalman filter, transfer-function and intervention models, unit root tests, cointegration test, volatility models (ARCH, GARCH, ARCH-M, GARCH-M, Taylor-Schwert GARCH, GJR,…
We consider machine learning techniques to develop low-latency approximate solutions to a class of inverse problems. More precisely, we use a probabilistic approach for the problem of recovering sparse stochastic signals that are members of…
Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for…
We attempt to unveil the fine structure of volatility feedback effects in the context of general quadratic autoregressive (QARCH) models, which assume that today's volatility can be expressed as a general quadratic form of the past daily…
Error entropy is a important nonlinear similarity measure, and it has received increasing attention in many practical applications. The default kernel function of error entropy criterion is Gaussian kernel function, however, which is not…
The discrete-time GARCH methodology which has had such a profound influence on the modelling of heteroscedasticity in time series is intuitively well motivated in capturing many `stylized facts' concerning financial series, and is now…
A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…
We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study…
Generalized autoregressive conditional heteroscedasticity (GARCH) models have long been considered as one of the most successful families of approaches for volatility modeling in financial return series. In this paper, we propose an…
We design the first fully-distributed algorithm for generalized Nash equilibrium seeking in aggregative games on a time-varying communication network, under partial-decision information, i.e., the agents have no direct access to the…
Gaussian mixture distributions are commonly employed to represent general probability distributions. Despite the importance of using Gaussian mixtures for uncertainty estimation, the entropy of a Gaussian mixture cannot be calculated…
Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. For Gaussian variables it is equivalent to transfer entropy, an information-theoretic measure of time-directed information transfer…
Fluctuations in parameters that are typically treated as fixed play a crucial role in the behavior of complex systems. However, to date, we lack a general non-equilibrium thermodynamic treatment of such a complex system. In this Letter, to…