James A. Feigenbaum

DISCRETE SCALE INVARIANCE IN STOCK MARKETS BEFORE CRASHES

We propose a picture of stock market crashes as critical points in a system with discrete scale invariance. The critical exponent is then complex, leading to log-periodic fluctuations in stock market indexes. We present “experimental” evidence in favor of this prediction. This picture is in the spirit of the known earthquake-stock market analogy and of recent work on log-periodic fluctuations associated with earthquakes.

A Leisurely Reading of the Life Cycle Consumption Data

A puzzle in consumption theory is the observation of a hump in age-consumption profiles. We study a general equilibrium life-cycle economy with capital in which households include both consumption and leisure in their period utility function. We calibrate the model and find that a significant hump in life-cycle consumption is a feature of the equilibrium. Thus inclusion of leisure in household preferences may provide part of the explanation of observed life-cycle consumption humps.

A Bayesian analysis of log-periodic precursors to financial crashes

A large number of papers have been written by physicists documenting an alleged signature of imminent financial crashes involving so-called log-periodic oscillations–oscillations which are periodic with respect to the logarithm of the time to the crash. In addition to the obvious practical implications of such a signature, log-periodicity has been taken as evidence that financial markets can be modelled as complex statistical-mechanics systems. However, while many log-periodic precursors have been identified, the statistical significance of these precursors and their predictive power remain controversial in part because log-periodicity is ill-suited for study with classical methods. This paper is the first effort to apply Bayesian methods in the testing of log-periodicity. Specifically, we focus on the Johansen–Ledoit–Sornette (JLS) model of log periodicity. Using data from the S&P 500 prior to the October 1987 stock market crash, we find that, if we do not consider crash probabilities, a null hypothesis model without log-periodicity outperforms the JLS model in terms of marginal likelihood. If we do account for crash probabilities, which has not been done in the previous literature, the JLS model outperforms the null hypothesis, but only if we ignore the information obtained by standard classical methods. If the JLS model is true, then parameter estimates obtained by curve fitting have small posterior probability. Furthermore, the data set contains negligible information about the oscillation parameters, such as the frequency parameter that has received the most attention in the previous literature.

More on a statistical analysis of log-periodic precursors to financial crashes

We respond to Sornette and Johansens criticisms of our findings regarding log-periodic precursors to financial crashes. Included in this paper are discussions of the Sornette-Johansen theoretical paradigm, traditional methods of identifying log-periodic precursors, the behaviour of the first differences of a log-periodic price series and the distribution of drawdowns for a securities price.

Detecting log-periodicity in a regime-switching model of stock returns

Log-periodic precursors have been identified before most and perhaps all financial crashes of the Twentieth Century, but efforts to statistically validate the leading model of log-periodicity, the Johansen–Ledoit–Sornette (JLS) model, have generally failed. The main feature of this model is that log-harmonic fluctuations in financial prices are driven by similar fluctuations in expected daily returns. Here we search more broadly for evidence of any log-periodic variation in expected daily returns by estimating a regime-switching model of stock returns in which the mean return fluctuates between a high and a low value. We find such evidence prior to the two largest drawdowns in the S&P 500 since 1950. However, if we estimate a log-harmonic specification for the stock index for the same time periods, fixing the frequency and critical time according to the results of the regime-switching model, the parameters do not satisfy restrictions imposed by the JLS model.

Lifecycle Dynamics of Income Uncertainty and Consumption

We propose a method for estimating household income uncertainty that does not impose restrictions on the underlying income shocks or assumptions about household behaviors. We measure income uncertainty as the variance of linear projection errors at various future horizons, up to 25 years ahead, conditional on only the information available to households when the projection is made. Our uncertainty estimates change substantially over the life cycle. We calibrate an income process to match our estimates, allowing the variances of both transitory and persistent shocks to change over the life cycle. Relative to previous studies, we find lower and less persistent income uncertainties that call for a life cycle consumption profile with a less pronounced hump.

Gravitational Analogues of Non-Linear BornElectrodynamics

Gravitational analogues of the nonlinear electrodynamics of Born and of Born and Infeld are introduced and applied to the black hole problem. This work is mainly devoted to the 2-dimensional case in which the relevant lagrangians are nonpolynomial in the scalar curvature.

A q‐deformation of the Coulomb problem

The algebra of observables of SOq(3)‐symmetric quantum mechanics is extended to include the inverse 1/R of the radial coordinate and used to obtain eigenvalues and eigenfunctions of a q‐deformed Coulomb Hamiltonian.

A Semiparametric Characterization of Income Uncertainty Over the Life Cycle

We propose a novel approach to estimate household income uncertainty at various future horizons and characterize how the estimated uncertainty evolves over the life cycle. We measure income uncertainty as the variance of linear forecast errors conditional on information available to households prior to observing the realized income. This approach is semiparametric because we impose essentially no restrictions on the statistical properties of the forecast errors. Relative to previous studies, we find lower and less persistent income uncertainties that call for a life cycle consumption profile with a less pronounced hump.

Household income uncertainties over three decades

We study the trend in household income uncertainty using a novel approach that measures income uncertainty at each future horizon as the variance of forecast errors without imposing specific parametric restrictions on the underlying income shocks. We document a widespread increase in household income uncertainty since the early 1970s that is both statistically and economically significant. For example, our measure of near-future uncertainty in total family non-capital income rose about 40% between 1971 and 2002. This rising uncertainty is likely due to the increase in variances of both persistent and transitory income shocks. A parsimoniously calibrated Aiyagari model is solved to illustrate how rising income uncertainty should have affected aggregate saving.