Quantifying economic fluctuations

This manuscript is a brief summary of a talk designed to address the question of whether two of the pillars of the field of phase transitions and critical phenomena—scale invariance and universality—can be useful in guiding research on interpreting empirical data on economic fluctuations. Using this conceptual framework as a guide, we empirically quantify the relation between trading activity—measured by the number of transactions N—and the price change G(t) for a given stock, over a time interval [t,t+Δt]. We relate the time-dependent standard deviation of price changes—volatility—to two microscopic quantities: the number of transactions N(t) in Δt and the variance W2(t) of the price changes for all transactions in Δt. We find that the long-ranged volatility correlations are largely due to those of N. We then argue that the tail-exponent of the distribution of N is insufficient to account for the tail-exponent of P{G>x}. Since N and W display only weak inter-dependency, our results show that the fat tails of the distribution P{G>x} arises from W. Finally, we review recent work on quantifying collective behavior among stocks by applying the conceptual framework of random matrix theory (RMT). RMT makes predictions for “universal” properties that do not depend on the interactions between the elements comprising the system, and deviations from RMT provide clues regarding system-specific properties. We compare the statistics of the cross-correlation matrix C—whose elements Cij are the correlation coefficients of price fluctuations of stock i and j—against a random matrix having the same symmetry properties. It is found that RMT methods can distinguish random and non-random parts of C. The non-random part of C which deviates from RMT results, provides information regarding genuine collective behavior among stocks. We also discuss results that are reminiscent of phase transitions in spin systems, where the divergent behavior of the response function at the critical point (zero magnetic field) leads to large fluctuations, and we discuss a curious “symmetry breaking”, a feature qualitatively identical to the behavior of the probability density of the magnetization for fixed values of the inverse temperature.