Related papers: A selective overview of nonparametric methods in f…
We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
In this paper we present numerical methods - finite differences and finite elements - for solution of partial differential equation of fractional order in time for one-dimensional space. This equation describes anomalous diffusion which is…
We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective…
Financial time series often exhibit low signal-to-noise ratio, posing significant challenges for accurate data interpretation and prediction and ultimately decision making. Generative models have gained attention as powerful tools for…
As the amount of economic and other data generated worldwide increases vastly, a challenge for future generations of econometricians will be to master efficient algorithms for inference in empirical models with large information sets. This…
This paper investigates a financial market where returns depend on an unobservable Gaussian drift process. While the observation of returns yields information about the underlying drift, we also incorporate discrete-time expert opinions as…
The author solves two problems: formation of object of econophysics, creation of the general theory of financial-economic monitoring. In the first problem he studied two fundamental tasks: a choice of conceptual model and creation of…
This paper compares and evaluates a set of non-parametric mutual information estimators with the goal of providing a novel toolset to progress in the analysis of the capacity of the nonlinear optical channel, which is currently an open…
The Fokker-Planck equation with diffusion coefficient quadratic in space variable, linear drift coefficient, and nonlocal nonlinearity term is considered in the framework of a model of analysis of asset returns at financial markets. For…
We suggest two nonparametric approaches, based on kernel methods and orthogonal series to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems, we derive optimal convergence…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
This survey is an introduction to asymptotic methods for portfolio-choice problems with small transaction costs. We outline how to derive the corresponding dynamic programming equations and simplify them in the small-cost limit. This allows…
In this review, we present econometric and statistical methods for analyzing randomized experiments. For basic experiments we stress randomization-based inference as opposed to sampling-based inference. In randomization-based inference,…
We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…
Despite the risk of misspecification they are tied to, parametric models continue to be used in statistical practice because they are accessible to all. In particular, efficient estimation procedures in parametric models are simple to…
We propose a stochastic volatility model for time series of curves. It is motivated by dynamics of intraday price curves that exhibit both between days dependence and intraday price evolution. The curves are suitably normalized to…
We consider a one-dimensional diffusion process $(X_t)$ which is observed at $n+1$ discrete times with regular sampling interval $\Delta$. Assuming that $(X_t)$ is strictly stationary, we propose nonparametric estimators of the drift and…
We present a new framework for modeling the statistical behavior of both fully developed turbulence and short-term dynamics of financial markets based on the nonextensive thermostatistics proposed by Tsallis. We also show that intermittency…
The financial market is nonpredictable, as according to the Bachelier, the mathematical expectation of the speculator is zero. Nevertheless, we observe in the price fluctuations the two distinct scales, short and long time. Behaviour of a…