Time-Varying Quantiles

A time-varying quantile can be fitted to a sequence of observations by formulating a time series model for the corresponding population quantile and iteratively applying a suitably modified state space signal extraction algorithm. Quantiles estimated in this way provide information on various aspects of a time series, including dispersion, asymmetry and, for financial applications, value at risk. Tests for the constancy of quantiles, and associated contrasts, are constructed using indicator variables; these tests have a similar form to stationarity tests and, under the null hypothesis, their asymptotic distributions belong to the Cramér von Mises family. Estimates of the quantiles at the end of the series provide the basis for forecasting. As such they offer an alternative to conditional quantile autoregressions and, at the same time, give some insight into their structure and potential drawbacks

Testing for the Presence of a Random Walk in Series with Structural Breaks - (Now published in Journal of Time Series Analysis, 22 (2001), pp.127-150.)

The paper considers tests for the presence of a random walk component in a stationary or trend stationary time series and extends them to series which contain structural breaks. The locally best invariant (LBI) test is derived and the asymptotic distribution obtained. Then a modified test statistic is proposed. The advantage of this statistic is that its asymptotic distribution is not dependent on the location of the breakpoint and its form is that of the generalised Cram?r-von Mises distribution, with degrees of freedom depending on the number of breakpoints. The performance of this modified test is shown, via some simulation experiments, to be comparable to that of the LBI test. An unconditional test, based on the assymption that there is a single break at an unknown point is also examined. The use of the tests is illustrated with data on the flow of the Nile and US Gross National Product.Brownian bridge, Cram?r-von Mises distribution, intervention analysis, locally best invariant test, structural time series model, unobserved components.

Polymeric Bladder for Storing Liquid Oxygen

A proposed system for storing oxygen in liquid form and dispensing it in gaseous form is based on (1) initial subcooling of the liquid oxygen; (2) containing the liquid oxygen in a flexible vessel; (3) applying a gas spring to the flexible vessel to keep the oxygen compressed above the saturation pressure and, thus, in the liquid state; and (4) using heat leakage into the system for vaporizing the oxygen to be dispensed. In a typical prior system based on these principles, the flexible vessel is a metal bellows housed in a rigid tank, and the gas spring consists of pressurized helium in the tank volume surrounding the bellows. Unfortunately, the welds in the bellows corrugations are subject to fatigue, and, because bellows have large ullage, a correspondingly large fraction of the oxygen content cannot be expelled. In the proposed system, the flexible vessel would be a bladder made of a liquid- crystal polymer (LCP). (LCPs are strong and compatible with liquid oxygen.) In comparison with a metal bellows, a polymeric bladder would have less ullage and would weigh less. In experiments involving fatigue cycling at liquid-nitrogen temperatures, two LCPs were found to be suitable for this application

Quantum Black Holes

Static solutions of large-$N$ quantum dilaton gravity in $1+1$ dimensions are analyzed and found to exhibit some unusual behavior. As expected from previous work, infinite-mass solutions are found describing a black hole in equilibrium with a bath of Hawking radiation. Surprisingly, the finite mass solutions are found to approach zero coupling both at the horizon and spatial infinity, with a ``bounce'' off of strong coupling in between. Several new zero mass solutions -- candidate quantum vacua -- are also described.Comment: 14 pages + 6 figure