High performance digital signal processing: Theory, design, and applications in finance

The way scientific research and business is conducted has drastically changed over the last decade. Big data and data-intensive scientific discovery are two terms that have been coined recently. They describe the tremendous amounts of noisy data, created extremely rapidly by various sensing devices and methods that need to be explored for information inference. Researchers and practitioners who can obtain meaningful information out of big data in the shortest time gain a competitive advantage. Hence, there is more need than ever for a variety of high performance computational tools for scientific and business analytics. Interest in developing efficient data processing methods like compression and noise filtering tools enabling real-time analytics of big data is increasing. A common concern in digital signal processing applications has been the lack of fast handling of observed data. This problem has been an active research topic being addressed by the progress in analytical tools allowing fast processing of big data. One particular tool is the Karhunen-Loève transform (KLT) (also known as the principal component analysis) where covariance matrix of a stochastic process is decomposed into its eigenvectors and eigenvalues as the optimal orthonormal transform. Specifically, eigenanalysis is utilized to determine the KLT basis functions. KLT is a widely employed signal analysis method used in applications including noise filtering of measured data and compression. However, defining KLT basis for a given signal covariance matrix demands prohibitive computational resources in many real-world scenarios. In this dissertation, engineering implementation of KLT as well as the theory of eigenanalysis for auto-regressive order one, AR(1), discrete stochastic processes are investigated and novel improvements are proposed. The new findings are applied to well-known problems in quantitative finance (QF). First, an efficient method to derive the explicit KLT kernel for AR(1) processes that utilizes a simple root finding method for the transcendental equations is introduced. Performance improvement over a popular numerical eigenanalysis algorithm, called divide and conquer, is shown. Second, implementation of parallel Jacobi algorithm for eigenanalysis on graphics processing units is improved such that the access to the dynamic random access memory is entirely coalesced. The speed is improved by a factor of 68.5 by the proposed method compared to a CPU implementation for a square matrix of size 1,024. Third, several tools developed and implemented in the dissertation are applied to QF problems such as risk analysis and portfolio risk management. In addition, several topics in QF, such as price models, Epps effect, and jump processes are investigated and new insights are suggested from a multi-resolution (multi-rate) signal processing perspective. It is expected to see this dissertation to make contributions in better understanding and bridging the analytical methods in digital signal processing and applied mathematics, and their wider utilization in the finance sector. The emerging joint research and technology development efforts in QF and financial engineering will benefit the investors, bankers, and regulators to build and maintain more robust and fair financial markets in the future