A Nonlinear Threshold Model for the Dependence of Extremes of Stationary Sequences

One of the main implications of the effcient market hypothesis (EMH) is that expected future returns on financial assets are not predictable if investors are risk neutral. In this paper we argue that financial time series offer more information than that this hypothesis seems to supply. In particular we postulate that runs of very large returns can be predictable for small time periods. In order to prove this we propose a TAR(3,1)-GARCH(1,1) model that is able to describe two different types of extreme events: a first type generated by large uncertainty regimes where runs of extremes are not predictable and a second type where extremes come from isolated dread/joy events. This model is new in the literature in nonlinear processes. Its novelty resides on two features of the model that make it different from previous TAR methodologies. The regimes are motivated by the occurrence of extreme values and the threshold variable is defined by the shock affecting the process in the preceding period. In this way this model is able to uncover dependence and clustering of extremes in high as well as in low volatility periods. This model is tested with data from General Motors stock prices corresponding to two crises that had a substantial impact in financial markets worldwide; the Black Monday of October 1987 and September 11th, 2001. By analyzing the periods around these crises we find evidence of statistical significance of our model and thereby of predictability of extremes for September 11th but not for Black Monday. These findings support the hypotheses of a big negative event producing runs of negative returns in the first case, and of the burst of a worldwide stock market bubble in the second example

dbar-approach to the dispersionless KP hierarchy

The dispersionless limit of the scalar nonlocal dbar-problem is derived. It is given by a special class of nonlinear first-order equations. A quasi-classical version of the dbar-dressing method is presented. It is shown that the algebraic formulation of dispersionless hierarchies can be expressed in terms of properties of Beltrami tupe equations. The universal Whitham hierarchy and, in particular, the dispersionless KP hierarchy turn out to be rings of symmetries for the quasi-classical dbar-problem.Comment: 13 pages, LaTex 24.9K

Atmospheric predictability of the martian atmosphere: from low-dimensional dynamics to operational forecasting?

Not available

Made-to-Measure models of the Galactic Box/Peanut bulge: stellar and total mass in the bulge region

We construct dynamical models of the Milky Way's Box/Peanut (B/P) bulge, using the recently measured 3D density of Red Clump Giants (RCGs) as well as kinematic data from the BRAVA survey. We match these data using the NMAGIC Made-to-Measure method, starting with N-body models for barred discs in different dark matter haloes. We determine the total mass in the bulge volume of the RCGs measurement (+-2.2 x +- 1.4 x +- 1.2 kpc) with unprecedented accuracy and robustness to be 1.84 +- 0.07 x10^10 Msun. The stellar mass in this volume varies between 1.25-1.6 x10^10 Msun, depending on the amount of dark matter in the bulge. We evaluate the mass-to-light and mass-to-clump ratios in the bulge and compare them to theoretical predictions from population synthesis models. We find a mass-to-light ratio in the K-band in the range 0.8-1.1. The models are consistent with a Kroupa or Chabrier IMF, but a Salpeter IMF is ruled out for stellar ages of 10 Gyr. To match predictions from the Zoccali IMF derived from the bulge stellar luminosity function requires about 40% or 0.7 x10^10 Msun dark matter in the bulge region. The BRAVA data together with the RCGs 3D density imply a low pattern speed for the Galactic B/P bulge of 25-30 km.s-1.kpc-1. This would place the Galaxy among the slow rotators (R >= 1.5). Finally, we show that the Milky Way's B/P bulge has an off-centred X structure, and that the stellar mass involved in the peanut shape accounts for at least 20% of the stellar mass of the bulge, significantly larger than previously thought.Comment: Accepted for publication in MNRA