3,902 research outputs found
New robust inference for predictive regressions
We propose two robust methods for testing hypotheses on unknown parameters of
predictive regression models under heterogeneous and persistent volatility as
well as endogenous, persistent and/or fat-tailed regressors and errors. The
proposed robust testing approaches are applicable both in the case of discrete
and continuous time models. Both of the methods use the Cauchy estimator to
effectively handle the problems of endogeneity, persistence and/or
fat-tailedness in regressors and errors. The difference between our two methods
is how the heterogeneous volatility is controlled. The first method relies on
robust t-statistic inference using group estimators of a regression parameter
of interest proposed in Ibragimov and Muller, 2010. It is simple to implement,
but requires the exogenous volatility assumption. To relax the exogenous
volatility assumption, we propose another method which relies on the
nonparametric correction of volatility. The proposed methods perform well
compared with widely used alternative inference procedures in terms of their
finite sample properties
Group Analysis of the Novikov Equation
We find the Lie point symmetries of the Novikov equation and demonstrate that
it is strictly self-adjoint. Using the self-adjointness and the recent
technique for constructing conserved vectors associated with symmetries of
differential equations, we find the conservation law corresponding to the
dilations symmetry and show that other symmetries do not provide nontrivial
conservation laws. Then we investigat the invariant solutions
Parameter estimation in pair hidden Markov models
This paper deals with parameter estimation in pair hidden Markov models
(pair-HMMs). We first provide a rigorous formalism for these models and discuss
possible definitions of likelihoods. The model being biologically motivated,
some restrictions with respect to the full parameter space naturally occur.
Existence of two different Information divergence rates is established and
divergence property (namely positivity at values different from the true one)
is shown under additional assumptions. This yields consistency for the
parameter in parametrization schemes for which the divergence property holds.
Simulations illustrate different cases which are not covered by our results.Comment: corrected typo
A symmetry classification for a class of (2+1)-nonlinear wave equation
In this paper, a symmetry classification of a -nonlinear wave equation
where is a smooth function on , using
Lie group method, is given. The basic infinitesimal method for calculating
symmetry groups is presented, and used to determine the general symmetry group
of this -nonlinear wave equation
Lattice Dynamics in the Half-Space, II. Energy Transport Equation
We consider the lattice dynamics in the half-space. The initial data are
random according to a probability measure which enforces slow spatial variation
on the linear scale . We establish two time regimes. For
times of order , , locally the measure
converges to a Gaussian measure which is time stationary with a covariance
inherited from the initial measure (non-Gaussian, in general). For times of
order , this covariance changes in time and is governed by a
semiclassical transport equation.Comment: 35 page
Conservation laws for self-adjoint first order evolution equations
In this work we consider the problem on group classification and conservation
laws of the general first order evolution equations. We obtain the subclasses
of these general equations which are quasi-self-adjoint and self-adjoint. By
using the recent Ibragimov's Theorem on conservation laws, we establish the
conservation laws of the equations admiting self-adjoint equations. We
illustrate our results applying them to the inviscid Burgers' equation. In
particular an infinite number of new symmetries of these equations are found
and their corresponding conservation laws are established.Comment: This manuscript has been accepted for publication in Journal of
Nonlinear Mathematical Physic
Ordinary differential equations which linearize on differentiation
In this short note we discuss ordinary differential equations which linearize
upon one (or more) differentiations. Although the subject is fairly elementary,
equations of this type arise naturally in the context of integrable systems.Comment: 9 page
Extreme value statistics and return intervals in long-range correlated uniform deviates
We study extremal statistics and return intervals in stationary long-range
correlated sequences for which the underlying probability density function is
bounded and uniform. The extremal statistics we consider e.g., maximum relative
to minimum are such that the reference point from which the maximum is measured
is itself a random quantity. We analytically calculate the limiting
distributions for independent and identically distributed random variables, and
use these as a reference point for correlated cases. The distributions are
different from that of the maximum itself i.e., a Weibull distribution,
reflecting the fact that the distribution of the reference point either
dominates over or convolves with the distribution of the maximum. The
functional form of the limiting distributions is unaffected by correlations,
although the convergence is slower. We show that our findings can be directly
generalized to a wide class of stochastic processes. We also analyze return
interval distributions, and compare them to recent conjectures of their
functional form
Noise resistance of stochastic image binding algorithms on the base of mutual information
Based on the mutual information of Shannon, Tsallis and Renyi, relay stochastic algorithms for image binding were synthesized and their stability and accuracy were studied
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