Empirical correlation matrix of asset returns has its intrinsic noise component. Eigen decomposition, also called Karhunen-Loeve Transform (KLT), is employed for noise filtering where an identified subset of eigenvalues replaced by zero. The filtered correlation matrix is utilized for...

Correlations of financial asset returns play a central role in designing investment portfolios by using Markowitz's modern portfolio theory (MPT). Correlations are calculated from asset prices that happen at various trading time intervals. Therefore, trading frequency dictates correlation...

Portfolio risk, introduced by Markowitz in 1952, and defined as the standard deviation of the portfolio return, is an important metric in the Modern Portfolio Theory (MPT). A popular method for portfolio selection is to manage the risk and return of a portfolio according to the...

Constant modulus transforms like discrete Fourier transform (DFT), Walsh transform, and Gold codes have been successfully used over several decades in several engineering applications, including discrete multi-tone (DMT), orthogonal frequency division multiplexing (OFDM) and code division...

In this paper, the eigendecomposition of a Toeplitz matrix populated by an exponential function in order to model empirical correlations of US equity returns is investigated. The closed-form expressions for eigenvalues and eigenvectors of such a matrix are available. These eigenvectors are used...

This paper discusses portfolio construction for investing in N given assets, e.g. constituents of the Dow Jones Industrial Average (DJIA) or large cap stocks, which is based on partitioning the investment universe into clusters. The clusters are determined from the trailing correlation matrix...

We propose sparse Karhunen-Loeve Transform (SKLT) method to sparse eigen subspaces. The sparsity (cardinality reduction) is achieved through the pdf-optimized quantization of basis function (vector) set. It may be considered an extension of the simple and soft thresholding (ST) methods. The...

Currently, there is a consensus among practitioners, industry veterans and academic researchers that the use of the state-of-the-art technology in financial sector including trading is inevitable, and HFT is generally beneficial. On the other hand, our collective memory reminds us that any...

The heuristic reasoning and experiments based design approach have been the pillars of studies on artificial neural networks. The explainable network performance is required for most applications. We focus on a simple classifier network for the two-class case of AR(1) data sources. We trace the...