Related papers: On some probabilistic properties of periodic GARCH…
This paper introduces one new multivariate volatility model that can accommodate an appropriately defined network structure based on low-frequency and high-frequency data. The model reduces the number of unknown parameters and the…
Network modeling characterizes the underlying principles of structural properties and is of vital significance for simulating dynamical processes in real world. However, bridging structure and dynamics is always challenging due to the…
Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in $R^d$. It is shown that natural parametrizations provide affine section…
Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do not occur for different classes of transformations. The main…
Strong consistency and asymptotic normality of the Gaussian pseudo-maximum likelihood estimate of the parameters in a wide class of ARCH$(\infty)$ processes are established. The conditions are shown to hold in case of exponential and…
A nonparametric procedure to estimate the conditional probability that a nonstationary geostatistical process exceeds a certain threshold value is proposed. The method consists of a bootstrap algorithm that combines conditional simulation…
The standard approach for studying the periodic ARMA model with coefficients that vary over the seasons is to express it in a vector form. In this paper we introduce an alternative method which views the periodic formulation as a time…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
Phase transitions generically occur in random matrix models as the parameters in the joint probability distribution of the random variables are varied. They affect all main features of the theory and the interpretation of statistical models…
The dynamics of granular media in the jammed, glassy region is described in terms of "modes", by applying a Principal Component Analysis (PCA) to the covariance matrix of the position of individual grains. We first demonstrate that this…
Point processes are stochastic models generating interacting points or events in time, space, etc. Among characteristics of these models, first-order intensity and conditional intensity functions are often considered. We focus on…
We consider a time inhomogeneous strong Markov process $(\xi_t)_{t\ge 0}$ taking values in a Polish state space whose semigroup has a $T$-periodic structure. We give simple conditions which imply ergodicity of the grid chain…
The paper introduces a new numerical characteristic of one dimensional stochastic systems. This quantity is a measure of minimal periodicity, can be detected in the process deep differential structure. The claim is that this new measure of…
This work develops asymptotic properties of a class of switching jump diffusion processes. The processes under consideration may be viewed as a number of jump diffusion processes modulated by a random switching mechanism. The underlying…
A simple variogram model with two parameters is presented that includes the power variogram for the fractional Brownian motion, a modified De Wijsian model, the generalized Cauchy model and the multiquadrics model. One parameter controls…
The Random Parameters model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we…
In this article, we discuss subgeometric ergodicity of a class of regime-switching diffusion processes. We derive conditions on the drift and diffusion coefficients, and the switching mechanism which result in subgeometric ergodicity of the…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
We provide conditions for the existence and the unicity of strictly stationary solutions of the usual Dynamic Conditional Correlation GARCH models (DCC-GARCH). The proof is based on Tweedie's (1988) criteria, after having rewritten…
The volatility of financial instruments is rarely constant, and usually varies over time. This creates a phenomenon called volatility clustering, where large price movements on one day are followed by similarly large movements on successive…