Relative Quantum Time

The need for a time-shift invariant formulation of quantum theory arises from fundamental symmetry principles as well as heuristic cosmological considerations. Such a description then leaves open the question of how to reconcile global invariance with the perception of change, locally. By introducing relative time observables, we are able to make rigorous the Page-Wootters conditional probability formalism to show how local Heisenberg evolution is compatible with global invariance

RELATIVE AGRICULTURAL PRICE CHANGES IN DIFFERENT TIME HORIZONS

Using a monthly data covering from 1974:1 to 2002:12, this paper explores the linkage between changes in macroeconomic variables (real exchange rate and inflation rate) and changes in relative agricultural prices in different time horizons (1, 12, 24, 36, 48, and 60 months). Controlling for factors likely to determine the long run trend of relative agricultural prices, the results show that long-term changes in real exchange rate has had a significant negative correlation with the long-term changes in relative agricultural prices. Conversely, changes of the general price have a role in explaining short-term changes in relative agricultural price at best.Demand and Price Analysis,

Crossover Time in Relative Fluctuations Characterizes the Longest Relaxation Time of Entangled Polymers

In entangled polymer systems, there are several characteristic time scales, such as the entanglement time and the disengagement time. In molecular simulations, the longest relaxation time (the disengagement time) can be determined by the mean square displacement (MSD) of a segment or by the shear relaxation modulus. Here, we propose the relative fluctuation analysis method, which is originally developed for characterizing large fluctuations, to determine the longest relaxation time from the center of mass trajectories of polymer chains (the time-averaged MSDs). Applying the method to simulation data of entangled polymers (by the slip-spring model and the simple reptation model), we provide a clear evidence that the longest relaxation time is estimated as the crossover time in the relative fluctuations.Comment: 17 pages, 9 figures, to appear in J. Chem. Phy

Relative entropy and waiting times for continuous-time Markov processes

For discrete-time stochastic processes, there is a close connection between return/waiting times and entropy. Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one does need a reference measure and so the natural object is relative entropy rather than entropy. In this paper we elaborate on this in the case of continuous-time Markov processes with finite state space. A reference measure of special interest is the one associated to the time-reversed process. In that case relative entropy is interpreted as the entropy production rate. The main results of this paper are: almost-sure convergence to relative entropy of suitable waiting-times and their fluctuation properties (central limit theorem and large deviation principle).Comment: 17 page

Time Dependent Relative Risk Aversion

Risk management and the thorough understanding of the relations between financial markets and the standard theory of macroeconomics have always been among the topics most addressed by researchers, both financial mathematicians and economists. This work aims at explaining investors’ behavior from a macroeconomic aspect (modeled by the investors’ pricing kernel and their relative risk aversion) using stocks and options data. Daily estimates of investors’ pricing kernel and relative risk aversion are obtained and used to construct and analyze a three-year long time-series. The first four moments of these time-series as well as their values at the money are the starting point of a principal component analysis. The relation between changes in a major index level and implied volatility at the money and between the principal components of the changes in relative risk aversion is found to be linear. The relation of the same explanatory variables to the principal components of the changes in pricing kernels is found to be log-linear, although this relation is not significant for all of the examined maturities.risk aversion, pricing kernels, time dependent preferences

The relative income hypothesis: does it exist over time? Evidence from the BHPS

The relative income hypothesis suggests that income inequality has a detrimental affect on people´s health. This previously well accepted relationship has recently come under scrutiny. Some claim it is a statistical artefact, while others argue that aggregate level data are not sophisticated enough to adequately test for its existence. This paper adds to the debate by estimating the relationship between income inequality and health using panel data. A random effects ordered probit is used to estimate the relationship between net household income, regional income inequality and self-reported health, for 3736 individuals over 9 years, while controlling for individual socioeconomic characteristics like gender, social class and age. Significant differences in income inequality across regions and considerable changes in health are found across years, however, the panel data estimating regressions find no significant association between any of the measures of income inequality and self-reported health. Therefore, it would appear that the relative income hypothesis does not exist over time and does not exist within Britain. Keywords: Self rated health, income inequalities, random effects ordered probit, BHPS