Breaking down the non-normality of daily stock returns

This paper investigates whether the non-normality typically observed in daily stock-market returns could arise because of the joint existence of breaks and GARCH effects. It proposes a data-driven procedure to credibly identify the number and timing of breaks and applies it on the benchmark stock-market indices of 27 OECD countries. The findings suggest that a substantial element of the observed deviations from normality might indeed be due to the co-existence of breaks and GARCH effects. However, the presence of structural changes is found to be the primary reason for the non-normality and not the GARCH effects. Also, there is still some remaining excess kurtosis that is unlikely to be linked to the specification of the conditional volatility or the presence of breaks. Finally, an interesting sideline result implies that GARCH models have limited capacity in forecasting stock-market volatility.

Asymptotic theory of wall-attached convection in a horizontal fluid layer with a vertical magnetic field

A horizontal fluid layer heated from below in the presence of a vertical magnetic field is considered. A simple asymptotic analysis is presented which demonstrates that a convection mode attached to the side walls of the layer sets in at Rayleigh numbers much below those required for the onset of convection in the bulk of the layer. The analysis complements an earlier analysis by Houchens [J. Fluid Mech. 469, 189 (2002)] which derived expressions for the critical Rayleigh number for the onset of convection in a vertical cylinder with an axial magnetic field in the cases of two aspect ratios. © 2008 American Institute of Physics.

Stokes waves revisited:exact solutions in the asymptotic limit

The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic “secular variation” in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.