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Goodness-of-fit test for long range dependent processes

Gilles Fay, Anne Philippe (2010)

ESAIM: Probability and Statistics

In this paper, we make use of the information measure introduced by Mokkadem (1997) for building a goodness-of-fit test for long-range dependent processes. Our test statistic is performed in the frequency domain and writes as a non linear functional of the normalized periodogram. We establish the asymptotic distribution of our statistic under the null hypothesis. Under specific alternative hypotheses, we prove that the power converges to one. The performance of our test procedure is illustrated...

Goodness-of-fit tests in long-range dependent processes under fixed alternatives

Holger Dette, Kemal Sen (2013)

ESAIM: Probability and Statistics

In a recent paper Fay and Philippe [ESAIM: PS 6 (2002) 239–258] proposed a goodness-of-fit test for long-range dependent processes which uses the logarithmic contrast as information measure. These authors established asymptotic normality under the null hypothesis and local alternatives. In the present note we extend these results and show that the corresponding test statistic is also normally distributed under fixed alternatives.

Growth-optimal portfolios under transaction costs

Jan Palczewski, Łukasz Stettner (2008)

Applicationes Mathematicae

This paper studies a portfolio optimization problem in a discrete-time Markovian model of a financial market, in which asset price dynamics depends on an external process of economic factors. There are transaction costs with a structure that covers, in particular, the case of fixed plus proportional costs. We prove that there exists a self-financing trading strategy maximizing the average growth rate of the portfolio wealth. We show that this strategy has a Markovian form. Our result is obtained...

Hölderian invariance principle for Hilbertian linear processes

Alfredas Račkauskas, Charles Suquet (2009)

ESAIM: Probability and Statistics

Let ( ξ n ) n ≥ 1 be the polygonal partial sums processes built on the linear processes X n = ∑ i ≥ 0 a i ( ϵ n - i ) , n ≥ 1, where ( ϵ i ) i ∈ ℤ are i.i.d., centered random elements in some separable Hilbert space ℍ and the ai's are bounded linear operators ℍ → ℍ , with ∑ i ≥ 0 ∥ a i ∥ < ∞ . We investigate functional central limit theorem for ξ n in the Hölder spaces H ρ o ( ℍ ) of functions x : [ 0 , 1 ] → ℍ such that ||x(t + h) - x(t)|| = o(p(h)) uniformly in t, where p(h) = hαL(1/h), 0 ≤ h ≤ 1 with 0 ≤ α ≤ 1/2 and L slowly varying at infinity. We obtain the H ρ o ( ℍ ) weak convergence of ξ n ...

Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix

Rémi Rhodes (2009)

Annales de l'I.H.P. Probabilités et statistiques

This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic one and a smoothly varying macroscopic one. The homogenization procedure aims to give a macroscopic approximation that takes into account the microscopic heterogeneities. This paper follows [Probab. Theory Related Fields (2009)] and improves this latter work by...

How to get Central Limit Theorems for global errors of estimates

Alain Berlinet (1999)

Applications of Mathematics

The asymptotic behavior of global errors of functional estimates plays a key role in hypothesis testing and confidence interval building. Whereas for pointwise errors asymptotic normality often easily follows from standard Central Limit Theorems, global errors asymptotics involve some additional techniques such as strong approximation, martingale theory and Poissonization. We review these techniques in the framework of density estimation from independent identically distributed random variables,...

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