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This paper presents a novel approach to stochastic volatility (SV) modeling by utilizing nonparametric techniques that enhance our ability to capture the volatility of financial time series data, with a particular emphasis on the…
Recent progress in image deblurring techniques focuses mainly on operating in both frequency and spatial domains using the Fourier transform (FT) properties. However, their performance is limited due to the dependency of FT on stationary…
Density functional theory (DFT) is an efficient instrument for describing a wide range of nanoscale phenomena: wetting transition, capillary condensation, adsorption, etc. In this paper, we suggest a method for obtaining the equilibrium…
Factorization machines (FMs) are a powerful tool for regression and classification in the context of sparse observations, that has been successfully applied to collaborative filtering, especially when side information over users or items is…
We define and study fractional versions of the well-known Gamma subordinator $\Gamma :=\{\Gamma (t),$ $t\geq 0\},$ which are obtained by time-changing $% \Gamma $ by means of an independent stable subordinator or its inverse. Their…
Fractional programming (FP) is a branch of mathematical optimization that deals with the optimization of ratios. It is an invaluable tool for signal processing and machine learning, because many key metrics in these fields are fractionally…
We propose the Value Gradient Sampler (VGS), a diffusion sampler parameterized by value functions. VGS generates samples from an unnormalized target density (i.e., energy) by evolving randomly initialized particles along the gradient of the…
As an old and widely used tool, it is still possible to find new insights and applications from Fast Fourier Transform (FFT)-based analyses. The FFT is frequently used to generate the Power Spectral Density (PSD) function, by squaring the…
Kernel-based modeling of dynamic systems has garnered a significant amount of attention in the system identification literature since its introduction to the field. While the method was originally applied to linear impulse response…
The fractional order grey models (FGM) have appealed considerable interest of research in recent years due to its higher effectiveness and flexibility than the conventional grey models and other prediction models. However, the definitions…
The Fractional Stochastic Regularity Model (FSRM) is an extension of Black-Scholes model describing the multifractal nature of prices. It is based on a multifractional process with a random Hurst exponent $H_t$, driven by a fractional…
Transformation-based methods have been an attractive approach in non-parametric inference for problems such as unconditional and conditional density estimation due to their unique hierarchical structure that models the data as flexible…
Based on a recent development in the area of error control coding, we introduce the notion of convolutional factor graphs (CFGs) as a new class of probabilistic graphical models. In this context, the conventional factor graphs are referred…
The paper proposes and implements a methodology to fit a seven-parameter Generalized Tempered Stable (GTS) distribution to financial data. The nonexistence of the mathematical expression of the GTS probability density function makes the…
Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. Our main result is that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of…
Discrete Fourier Transform Test (DFTT), which is a randomness test included in NIST SP800-22, has a problem. It is that theoretical reference distribution of the test statistic has not been derived. In this paper, we propose a new test…
The linear fractional stable motion (LFSM) extends the fractional Brownian motion (fBm) by considering $\alpha$-stable increments. We propose a method to forecast future increments of the LFSM from past discrete-time observations, using the…
Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model…
The notion of fractional Fourier transform (FrFT) has been used and investigated for many years by various research communities, which finds widespread applications in many diverse fields of research study. The potential applications…
Stochastic volatility modelling of financial processes has become increasingly popular. The proposed models usually contain a stationary volatility process. We will motivate and review several nonparametric methods for estimation of the…