On the derivatives of generalized Gegenbauer polynomials

We prove some new formulae for the derivatives of the generalized Gegenbauer polynomials associated to the Lie algebra $A_2$.Comment: 3 pages, no figures; submitted to Theor. Math. Phy

On forecasting daily stock volatility: the role of intraday information and market conditions

Several recent studies advocate the use of nonparametric estimators of daily price vari- ability that exploit intraday information. This paper compares four such estimators, realised volatility, realised range, realised power variation and realised bipower variation, by examining their in-sample distributional properties and out-of-sample forecast ranking when the object of interest is the conventional conditional variance. The analysis is based on a 7-year sample of transaction prices for 14 NYSE stocks. The forecast race is conducted in a GARCH framework and relies on several loss functions. The realized range fares relatively well in the in-sample .t analysis, for instance, regarding the extent to which it brings normality in returns. However, overall the realised power variation provides the most accurate 1-day-ahead forecasts. Fore- cast combination of all four intraday measures produces the smallest forecast errors in about half of the sampled stocks. A market conditions analysis reveals that the additional use of intraday data on day t .. 1 to forecast volatility on day t is most advantageous when day t is a low volume or an up-market day. The results have implications for value-at-risk analysis.

Explicit computations of low lying eigenfunctions for the quantum trigonometric Calogero-Sutherland model related to the exceptional algebra E7

In the previous paper math-ph/0507015 we have studied the characters and Clebsch-Gordan series for the exceptional Lie algebra E7 by relating them to the quantum trigonometric Calogero-Sutherland Hamiltonian with coupling constant K=1. Now we extend that approach to the case of general K

Sieve bootstrap t-tests on long-run average parameters

Panel estimators can provide consistent measures of a long-run average parameter even if the individual regressions are spurious. However, the t-test on this parameter is fraught with problems because the limit distribution of the test statistic is non-standard and rather complicated, particularly in panels with mixed (non-)stationary errors. A sieve bootstrap framework is suggested to approximate the distribution of the t-statistic. An extensive Monte Carlo study demonstrates that the bootstrap is quite useful in this context

Emerging Market Sovereign Credit Spreads: In-Sample and Out-of-Sample Predictability

This paper investigates the quarter-ahead predictability of Brazil, Mexico, Philippines and Turkey credit spreads for short and long maturity bonds during two separate periods preceding and following the Lehman Brothers' default. A model based on the current country-specific credit spread curve predicts no better than the random walk and slope regression benchmarks. Extensions with the global yield curve factors and short-term interest rate volatility notably outperform the benchmark models post-Lehman. Our findings suggest that uncertainty indicators, both global and domestic, contain information about future credit spreads and that bond prices did better align with fundamentals post-crisis

One-loop mass shift formula for kinks and self-dual vortices

A formula is derived that allows us to compute one-loop mass shifts for kinks and self-dual Abrikosov-Nielsen-Olesen vortices. The procedure is based in canonical quantization and heat kernel/zeta function regularization methods.Comment: LaTex file, 8 pages, 1 figure . Based on a talk given by J. M. G. at the 7th Workshop on Quantum Field Theory under the Influence of External Conditions (QFEXT05), Barcelona, Spain. Minor corrections. Version to appear in Journal of Physics

Quantum corrections to the mass of self-dual vortices

The mass shift induced by one-loop quantum fluctuations on self-dual ANO vortices is computed using heat kernel/generalized zeta function regularization methods.Comment: 4 pages RevTex, version to appear in Physical Review

Quantum fluctuations around low-dimensional topological defects

In these Lectures a method is described to analyze the effect of quantum fluctuations on topological defect backgrounds up to the one-loop level. The method is based on the spectral heat kernel/zeta function regularization procedure, and it is first applied to various types of kinks arising in several deformed linear and non-linear sigma models with different numbers of scalar fields. In the second part, the same conceptual framework is constructed for the topological solitons of the planar semilocal Abelian Higgs model, built from a doublet of complex scalar fields and one U(1) gauge field.Comment: 63 pages, 14 figures, expanded version of two lectures given by J.M.G. in 5th International School on Field Theory and Gravitation, Cuiaba, Brazi