2,611 research outputs found
Exact Simulation of Wishart Multidimensional Stochastic Volatility Model
In this article, we propose an exact simulation method of the Wishart
multidimensional stochastic volatility (WMSV) model, which was recently
introduced by Da Fonseca et al. \cite{DGT08}. Our method is based onanalysis of
the conditional characteristic function of the log-price given volatility
level. In particular, we found an explicit expression for the conditional
characteristic function for the Heston model. We perform numerical experiments
to demonstrate the performance and accuracy of our method. As a result of
numerical experiments, it is shown that our new method is much faster and
reliable than Euler discretization method.Comment: 27 page
Random fields of multivariate test statistics, with applications to shape analysis
Our data are random fields of multivariate Gaussian observations, and we fit
a multivariate linear model with common design matrix at each point. We are
interested in detecting those points where some of the coefficients are nonzero
using classical multivariate statistics evaluated at each point. The problem is
to find the -value of the maximum of such a random field of test statistics.
We approximate this by the expected Euler characteristic of the excursion set.
Our main result is a very simple method for calculating this, which not only
gives us the previous result of Cao and Worsley [Ann. Statist. 27 (1999)
925--942] for Hotelling's , but also random fields of Roy's maximum root,
maximum canonical correlations [Ann. Appl. Probab. 9 (1999) 1021--1057],
multilinear forms [Ann. Statist. 29 (2001) 328--371], [Statist.
Probab. Lett 32 (1997) 367--376, Ann. Statist. 25 (1997) 2368--2387] and
scale space [Adv. in Appl. Probab. 33 (2001) 773--793]. The trick
involves approaching the problem from the point of view of Roy's
union-intersection principle. The results are applied to a problem in shape
analysis where we look for brain damage due to nonmissile trauma.Comment: Published in the Annals of Statistics (http://www.imstat.org/aos/) by
the Institute of Mathematical Statistics (http://www.imstat.org
Systematics of Aligned Axions
We describe a novel technique that renders theories of axions tractable,
and more generally can be used to efficiently analyze a large class of periodic
potentials of arbitrary dimension. Such potentials are complex energy
landscapes with a number of local minima that scales as , and so for
large appear to be analytically and numerically intractable. Our method is
based on uncovering a set of approximate symmetries that exist in addition to
the periods. These approximate symmetries, which are exponentially close to
exact, allow us to locate the minima very efficiently and accurately and to
analyze other characteristics of the potential. We apply our framework to
evaluate the diameters of flat regions suitable for slow-roll inflation, which
unifies, corrects and extends several forms of "axion alignment" previously
observed in the literature. We find that in a broad class of random theories,
the potential is smooth over diameters enhanced by compared to the
typical scale of the potential. A Mathematica implementation of our framework
is available online.Comment: 68 pages, 17 figure
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