Related papers: On discrete stochastic processes with long-lasting…
Count time series data are frequently analyzed by modeling their conditional means and the conditional variance is often considered to be a deterministic function of the corresponding conditional mean and is not typically modeled…
Inspired by the recent literature on aggregation theory, we aim at relating the long range correlation of the stocks return volatility to the heterogeneity of the investors' expectations about the level of the future volatility. Based on a…
In time-dependent density-functional theory, exchange and correlation (xc) beyond the adiabatic local density approximation can be described in terms of viscoelastic stresses in the electron liquid. In the time domain, this leads to a…
By considering special sampling of discrete scale invariant (DSI) processes we provide a sequence which is in correspondence to multi-dimensional self-similar process. By imposing Markov property we show that the covariance functions of…
We introduce a wide family of stochastic processes that are obtained as sums of self-similar localized "waveforms" with multiplicative intensity in the spirit of the Richardson cascade picture of turbulence. We establish the convergence and…
Longitudinal data are important in numerous fields, such as healthcare, sociology and seismology, but real-world datasets present notable challenges for practitioners because they can be high-dimensional, contain structured missingness…
We consider a measure of dependence for symmetric $\alpha$-stable random vectors, which was introduced by the author in 1976. We demonstrate that this measure of dependence can be extended for much more broad class of random vectors (up to…
The persistence of a stochastic variable is the probability that it does not cross a given level during a fixed time interval. Although persistence is a simple concept to understand, it is in general hard to calculate. Here we consider zero…
The spatial dependence in mean has been well studied by plenty of models in a large strand of literature, however, the investigation of spatial dependence in variance is lagging significantly behind. The existing models for the spatial…
Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an…
We introduce a class of discrete random walk model driven by global memory effects. At any time the right-left transitions depend on the whole previous history of the walker, being defined by an urn-like memory mechanism. The characteristic…
Even simply-defined, finite-state generators produce stochastic processes that require tracking an uncountable infinity of probabilistic features for optimal prediction. For processes generated by hidden Markov chains the consequences are…
This paper studies some temporal dependence properties and addresses the issue of parametric estimation for a class of state-dependent autoregressive models for nonlinear time series in which we assume a stochastic autoregressive…
In this paper the class of ARCH$(\infty)$ models is generalized to the nonstationary class of ARCH$(\infty)$ models with time-varying coefficients. For fixed time points, a stationary approximation is given leading to the notation ``locally…
In many problem settings, parameter vectors are not merely sparse but dependent in such a way that non-zero coefficients tend to cluster together. We refer to this form of dependency as "region sparsity." Classical sparse regression…
A statistical model of discrete finite length random processes with negative power law spectral densities is presented. The definition of terms is followed by a description of the spectral density trend. An algorithmic construction of…
Linear regressions with endogeneity are widely used to estimate causal effects. This paper studies a framework that involves two common practical issues: endogeneity of the regressors and heteroskedasticity that depends on endogenous…
Hawkes processes are a class of self-exciting point processes that are used to model complex phenomena. While most applications of Hawkes processes assume that event data occurs in continuous-time, the less-studied discrete-time version of…
In this paper, we consider the classic stochastic (dynamic) knapsack problem, a fundamental mathematical model in revenue management, with general time-varying random demand. Our main goal is to study the optimal policies, which can be…
We study the dependence of volatility on the stock price in the stochastic volatility framework on the example of the Heston model. To be more specific, we consider the conditional expectation of variance (square of volatility) under fixed…