Multivariate cumulants in outlier detection for financial data analysis

There are many research papers yielding the financial data models, where returns are tied either to the fundamental analysis or to the individual, often irrational, behaviour of investors. In the second case the bubble followed by the crisis is possible on the market. Such bubble or crisis is reflected by the cross-correlated extreme positive or negative returns of many assets. Such returns are modelled by the copula with the meaningful tail dependencies. The typical model of such cross-correlation provides the t-Student copula. The author demonstrates that the mutual information tied to this copula can be measured by the 4th order multivariate cumulants. Tested on the artificial data, the 4th order multivariate cumulant approach was used successfully for the financial crisis detection. For this end the author introduces the outliers detection algorithm. In addition this algorithm displays the potential application for the crisis prediction, where the cross-correlated extreme events may appear before the crisis in the analogy to the auto-correlated ones measured by the Hurst Exponent

Improving Detection of Dim Targets: Optimization of a Moment-based Detection Algorithm

Wide area motion imagery (WAMI) sensor technology is advancing rapidly. Increases in frame rates and detector array sizes have led to a dramatic increase in the volume of data that can be acquired. Without a corresponding increase in analytical manpower, much of these data remain underutilized. This creates a need for fast, automated, and robust methods for detecting dim, moving signals of interest. Current approaches fall into two categories: detect-before-track (DBT) and track-before-detect (TBD) methods. The DBT methods use thresholding to reduce the quantity of data to be processed, making real time implementation practical but at the cost of the ability to detect low signal to noise ratio (SNR) targets without acceptance of a high false alarm rate. TBD methods exploit both the temporal and spatial information simultaneously to make detection of low SNR targets possible, but at the cost of computation time. This research seeks to contribute to the near real time detection of low SNR, unresolved moving targets through an extension of earlier work on higher order moments anomaly detection, a method that exploits both spatial and temporal information but is still computationally efficient and massively parallellizable. The MBD algorithm was found to detect targets comparably with leading TBD methods in 1000th the time