Economic sector identification in a set of stocks traded at the New York Stock Exchange: a comparative analysis

We review some methods recently used in the literature to detect the existence of a certain degree of common behavior of stock returns belonging to the same economic sector. Specifically, we discuss methods based on random matrix theory and hierarchical clustering techniques. We apply these methods to a set of stocks traded at the New York Stock Exchange. The investigated time series are recorded at a daily time horizon. All the considered methods are able to detect economic information and the presence of clusters characterized by the economic sector of stocks. However, different methodologies provide different information about the considered set. Our comparative analysis suggests that the application of just a single method could not be able to extract all the economic information present in the correlation coefficient matrix of a set of stocks.Comment: 13 pages, 8 figures, 2 Table

Sector identification in a set of stock return time series traded at the London Stock Exchange

We compare some methods recently used in the literature to detect the existence of a certain degree of common behavior of stock returns belonging to the same economic sector. Specifically, we discuss methods based on random matrix theory and hierarchical clustering techniques. We apply these methods to a portfolio of stocks traded at the London Stock Exchange. The investigated time series are recorded both at a daily time horizon and at a 5-minute time horizon. The correlation coefficient matrix is very different at different time horizons confirming that more structured correlation coefficient matrices are observed for long time horizons. All the considered methods are able to detect economic information and the presence of clusters characterized by the economic sector of stocks. However different methods present a different degree of sensitivity with respect to different sectors. Our comparative analysis suggests that the application of just a single method could not be able to extract all the economic information present in the correlation coefficient matrix of a stock portfolio.Comment: 28 pages, 13 figures, 3 Tables. Proceedings of the conference on "Applications of Random Matrices to Economy and other Complex Systems", Krakow (Poland), May 25-28 2005. Submitted for pubblication to Acta Phys. Po

A Comparative Study of Pairwise Learning Methods based on Kernel Ridge Regression

Many machine learning problems can be formulated as predicting labels for a pair of objects. Problems of that kind are often referred to as pairwise learning, dyadic prediction or network inference problems. During the last decade kernel methods have played a dominant role in pairwise learning. They still obtain a state-of-the-art predictive performance, but a theoretical analysis of their behavior has been underexplored in the machine learning literature. In this work we review and unify existing kernel-based algorithms that are commonly used in different pairwise learning settings, ranging from matrix filtering to zero-shot learning. To this end, we focus on closed-form efficient instantiations of Kronecker kernel ridge regression. We show that independent task kernel ridge regression, two-step kernel ridge regression and a linear matrix filter arise naturally as a special case of Kronecker kernel ridge regression, implying that all these methods implicitly minimize a squared loss. In addition, we analyze universality, consistency and spectral filtering properties. Our theoretical results provide valuable insights in assessing the advantages and limitations of existing pairwise learning methods.Comment: arXiv admin note: text overlap with arXiv:1606.0427

Identifying States of a Financial Market

The understanding of complex systems has become a central issue because complex systems exist in a wide range of scientific disciplines. Time series are typical experimental results we have about complex systems. In the analysis of such time series, stationary situations have been extensively studied and correlations have been found to be a very powerful tool. Yet most natural processes are non-stationary. In particular, in times of crisis, accident or trouble, stationarity is lost. As examples we may think of financial markets, biological systems, reactors or the weather. In non-stationary situations analysis becomes very difficult and noise is a severe problem. Following a natural urge to search for order in the system, we endeavor to define states through which systems pass and in which they remain for short times. Success in this respect would allow to get a better understanding of the system and might even lead to methods for controlling the system in more efficient ways. We here concentrate on financial markets because of the easy access we have to good data and because of the strong non-stationary effects recently seen. We analyze the S&P 500 stocks in the 19-year period 1992-2010. Here, we propose such an above mentioned definition of state for a financial market and use it to identify points of drastic change in the correlation structure. These points are mapped to occurrences of financial crises. We find that a wide variety of characteristic correlation structure patterns exist in the observation time window, and that these characteristic correlation structure patterns can be classified into several typical "market states". Using this classification we recognize transitions between different market states. A similarity measure we develop thus affords means of understanding changes in states and of recognizing developments not previously seen.Comment: 9 pages, 8 figure