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

Generating functions and multiplicity formulas: the case of rank two simple Lie algebras

A procedure is described that makes use of the generating function of characters to obtain a new generating function $H$ giving the multiplicities of each weight in all the representations of a simple Lie algebra. The way to extract from $H$ explicit multiplicity formulas for particular weights is explained and the results corresponding to rank two simple Lie algebras shown

On the generating function of weight multiplicities for the representations of the Lie algebra C2C_2

We use the generating function of the characters of $C_2$ to obtain a generating function for the multiplicities of the weights entering in the irreducible representations of that simple Lie algebra. From this generating function we derive some recurrence relations among the multiplicities and a simple graphical recipe to compute them.Comment: arXiv admin note: text overlap with arXiv:1304.720

Combined photo- and electroreflectance of multijunction solar cells enabled by subcell electric coupling

Electric coupling between subcells of a monolithically grown multijunction solar cell in short circuit allows their simultaneous and independent characterization by means of photo- and electroreflectance. The photovoltage generated by selective absorption of the pump beam in a given subcell during photoreflectance measurements results in reverse biasing the complementary subunits at the modulation frequency set on the pump illumination. Such voltage bias modulation acts then as external perturbation on the complementary subcells. The spectral separation of the different subcell absorption ranges permits the probe beam to record in a single spectrum the response of the complete device as a combination of photo- and electroreflectance, thereby providing access for diagnosis of subcells on an individual basis. This form of modulation spectroscopy is demonstrated on a GaInP/GaAs tandem solar cell.Comment: 5 pages, 4 figures. This article has been accepted by Appl. Phys. Lett. After it is published, it will be found at https://doi.org/10.1063/1.506260

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