Construction of embedded fMRI resting state functional connectivity networks using manifold learning

We construct embedded functional connectivity networks (FCN) from benchmark resting-state functional magnetic resonance imaging (rsfMRI) data acquired from patients with schizophrenia and healthy controls based on linear and nonlinear manifold learning algorithms, namely, Multidimensional Scaling (MDS), Isometric Feature Mapping (ISOMAP) and Diffusion Maps. Furthermore, based on key global graph-theoretical properties of the embedded FCN, we compare their classification potential using machine learning techniques. We also assess the performance of two metrics that are widely used for the construction of FCN from fMRI, namely the Euclidean distance and the lagged cross-correlation metric. We show that the FCN constructed with Diffusion Maps and the lagged cross-correlation metric outperform the other combinations

Detecting a Currency's Dominance or Dependence using Foreign Exchange Network Trees

In a system containing a large number of interacting stochastic processes, there will typically be many non-zero correlation coefficients. This makes it difficult to either visualize the system's inter-dependencies, or identify its dominant elements. Such a situation arises in Foreign Exchange (FX) which is the world's biggest market. Here we develop a network analysis of these correlations using Minimum Spanning Trees (MSTs). We show that not only do the MSTs provide a meaningful representation of the global FX dynamics, but they also enable one to determine momentarily dominant and dependent currencies. We find that information about a country's geographical ties emerges from the raw exchange-rate data. Most importantly from a trading perspective, we discuss how to infer which currencies are `in play' during a particular period of time

Kernel methods for detecting coherent structures in dynamical data

We illustrate relationships between classical kernel-based dimensionality reduction techniques and eigendecompositions of empirical estimates of reproducing kernel Hilbert space (RKHS) operators associated with dynamical systems. In particular, we show that kernel canonical correlation analysis (CCA) can be interpreted in terms of kernel transfer operators and that it can be obtained by optimizing the variational approach for Markov processes (VAMP) score. As a result, we show that coherent sets of particle trajectories can be computed by kernel CCA. We demonstrate the efficiency of this approach with several examples, namely the well-known Bickley jet, ocean drifter data, and a molecular dynamics problem with a time-dependent potential. Finally, we propose a straightforward generalization of dynamic mode decomposition (DMD) called coherent mode decomposition (CMD). Our results provide a generic machine learning approach to the computation of coherent sets with an objective score that can be used for cross-validation and the comparison of different methods

Evidence on the Economics of Equity Return Volatility Clustering

The underlying economic sources of volatility clustering in asset returns remain a puzzle in financial economics. Using daily equity returns, we study variation in the volatility relation between the conditional variance of individual firm returns and yesterday's market return shock. We find a number of regularities in this market-to-firm volatility relation. (1) It decreases following macroeconomic news announcements; (2) it does not change systematically during the high-news months when firms announce quarterly earnings; and (3) it increases substantially with our measures of dispersion-in-beliefs across traders about the market's common-factor signal. Our evidence suggests that volatility-clustering is a natural result of a price formation process with heterogeneous beliefs across traders, and that volatility clustering is not attributable to an autocorrelated news-generation process around public information such as macroeconomic news releases or firms' earnings releases. We find consistent results in our sample of large-capitalization firms in Japan and the U.K., which suggests a generality of our results and bolsters our economic interpretation.

Pay growth, fairness and job satisfaction : implications for nominal and real wage rigidity

Theories of wage rigidity often rely on a positive relationship between pay changes and utility, arising from concern for fairness or gift exchange. Supportive evidence has emerged from laboratory experiments, but the link has not yet been established with field data. This paper contributes a first step, using representative British data. Workers care about the level and the growth of earnings. Below-median wage increases lead to an insult effect except when similar workers have real wage reductions or frm production is falling. Nominal pay cuts appear insulting even when the firm is doing badly