This paper presents a multinomial theorem on the binomial coefficients for combinatorial geometric series. The coefficient for each term in combinatorial geometric series refers to a binomial coefficient. These ideas can enable the scientific researchers to solve the real life problems

This paper presents the summations and sums of Single terms and successive terms of geometric series with negative exponents (negative powers). This idea will be useful for researchers who are involving in solving the scientific problems

This paper present computation of the summation of geometric series in an innovative way. Geometric series is a computational method which is used for numerous applications in science, engineering, and medicine. The geometric series and exponential decay model have already been used as...

In this paper we address the issue of assessing and communicating the joint probabilities implied by density forecasts from multivariate time series models. We focus our attention in three areas. First, we investigate a new method of producing fan charts that better communicates the uncertainty...

MTSS-GAN is a new generative adversarial network (GAN) developed to simulate diverse multivariate time series (MTS) data with finance applications in mind. The purpose of this synthesiser is two-fold, we both want to generate data that accurately represents the original data, while also having...

Demonstration that noise filtered correlation matrices can be used for early detection of a regime change in temporal behavior of securities. This demonstration was carried out for a portfolio of 40 S&P500 securities with just two, randomly chosen, securities undergoing a deliberately arranged...

Demonstration that our noise filtering procedure is extremely robust on the basis of the following experiment. The noise filtering procedure was applied first to an empirical correlation matrix and, second, to the matrix built from the same time series deliberately contaminated with noise. The...

Demonstration that our noise filtering procedure is extremely robust on the basis of the following experiment. The noise filtering procedure was applied first to an empirical correlation matrix and, second, to the same matrix deliberately contaminated with noise. The final, noise filtered...

Demonstration of the omnipresence of noise in financial correlation/covariance matrices revealed by means of random matrix theory, a branch of probability theory.Introduction of the Shannon entropy as a measure of noise in correlation matrices. Demonstration of substantial entropy decrease as a...

Alexander Izmailov, Ph.D (theoretical physics) and Brian Shay, Ph.D (mathematics) of Market Memory Trading, L.L.C. present, in a series of nine (9) white papers, aspects of a revolutionary advance in uncovering hidden dependencies via filtering noise from correlation matrices developed by the...