112 research outputs found
Distribution-free specification tests of conditional models
Get PDFThis article proposes a class of asymptotically distribution-free specification tests for parametric conditional distributions. These tests are based on a martingale transform of a proper sequential empirical process of conditionally transformed data. Standard continuous functionals of this martingale provide omnibus tests while linear combinations of the orthogonal components in its spectral representation form a basis for directional tests. Finally, Neyman-type smooth tests, a compromise between directional and omnibus tests, are discussed. As a special example we study in detail the construction of directional tests for the null hypothesis of conditional normality versus heteroskedastic contiguous alternatives. A small Monte Carlo study shows that our tests attain the nominal level already for small sample sizes.Publicad
From statistics to mathematical finance: festschrift in honour of Winfried Stute
No full textThis book, dedicated to Winfried Stute on the occasion of his 70th birthday, presents a unique collection of contributions by leading experts in statistics, stochastic processes, mathematical finance and insurance. The individual chapters cover a wide variety of topics ranging from nonparametric estimation, regression modelling and asymptotic bounds for estimators, to shot-noise processes in finance, option pricing and volatility modelling. The book also features review articles, e.g. on survival analysis
Applications of Mellin-Barnes Integrals to Deconvolution Problems
Get PDFIn this thesis we study the additive model of errors in variables, which is also known as the deconvolution problem. The objective consists particularly in the reconstruction of the distribution F associated with a random variable X, which is observable only through a sample of a blurred variable Y, due to an additive random error ε with known distribution H. Our initial considerations yield an unbiased estimator for F for various discrete and some continuous distributions. A more general approach then leads us to the symmetrized model of errors in variables. It is obtained by an additional convolution of G with the conjugate error distribution of H, thereby resulting in an error distribution of symmetric type. As a consequence the characteristic function of X can be represented as the limit of a geometric series. By truncation of this series we deduce an approximation of F, which is valid for arbitrary error distributions. This approximation, termed the deconvolution function, converges to F in many cases. To determine the corresponding rates of convergence, techniques from complex calculus and particularly Mellin-Barnes integrals turn out to be appropriate. The latter describe a special class of integrals that can be evaluated by residue analysis. The results are established in a more general setting, which makes them applicable to other Laplace-type integrals. With the aid of the deconvolution function we also construct an estimator for F. The asymptotic properties of its variance, a peculiar integral of dimension two, can be specified by virtue of our findings from the concluding chapter. These results rely on iterated Mellin-Barnes integrals.Sonstige Drittmittelgeber/-inne
Martingaltransformationen von Punktprozessen und ihre Anwendungen
No full textNon-negative martingales represent an important aspect of process the- ory. The main contribution of this thesis is to present methods to transform a general point process N, characterized by its conditional intensity λ, into a process that satisfies the properties of a non-negative martingale. The resulting systems allow the development of techniques for the investigation of statistical problems.
Historically, martingale transformations have been studied for the first time with respect to Ito processes. In this case, where the triggering process is a Brownian motion, a backward heat equation must be solved. This theory has evolved successfully over several decades and can now be formulated in a generalized form for semimartingales.
In the present work, these results are used, among other things, to generalize martingales that are already known in connection with the empirical distribution function. Within this approach, various solutions arise, whose associated processes exhibit different characteristics. This allows us to have a natural access to the class of Poisson-Charlier functions as a solution to the differential equation for the case of a Poisson process. The Poisson-Charlier functions are further generalized in a subsequent step for more general point processes. To generate non-negative martingales, we also make use of the integral representation for martingales by imposing characteristic properties on the generating predictable processes
Statistical properties and economic implications of Jump-Diffusion Processes with Shot-Noise effects
Get PDFThis paper analyzes the Shot-Noise Jump-Diffusion model of Altmann, Schmidt and Stute (2008), which
introduces a new situation where the effects of the arrival of rare, shocking information to the financial
markets may fade away in the long run. We analyze several economic implications of the model,
providing an analytical expression for the process distribution. We also prove that certain specifications
of this model can provide negative serial persistence. Additionally, we find that the degree of serial
autocorrelation is related to the arrival and magnitude of abnormal information. Finally, a GMM
framework is proposed to estimate the model parameters
Statistical Properties and Economic Implications of Jump-Diffusion Processes with Shot-Noise Effects
Get PDFThis paper analyzes the Shot-Noise Jump-Diffusion model of Altmann, Schmidt and Stute (2008), which introduces a new situation where the effects of the arrival of rare, shocking information to the financial markets may fade away in the long run. We analyze several economic implications of the model, providing an analytical expression for the process distribution. We also prove that certain specifications of this model can provide negative serial persistence. Additionally, we find that the degree of serial autocorrelation is related to the arrival and magnitude of abnormal information. Finally, a GMM framework is proposed to estimate the model parameters.Filtered Poisson Process, Characteristic Function, Generalized Method of Moments
Essays on specification tests for conditional hazard and distribution models
Get PDFPrograma de Doctorado en Economía por la Universidad Carlos III de MadridPresidente: Winfried Stute; Secretario: Carlos Velasco Gómez; Vocal: Javier Hidalg
On a class of stopping times for M-estimators
No full textAbstractFor a given score function ψ = ψ(x, θ), let θn be Huber's M-estimator for an unknown population parameter θ. Under some mild smoothness assumptions it is known that n12(θn − θ) is asymptotically normal. In this paper the stopping times τc(m) = inf{n ≥ m: n12 |θn − θ | > c } associated with the sequence of confidence intervals for θ are investigated. A useful representation of M-estimators is derived, which is also appropriate for proving laws of the iterated logarithm and Donskertype invariance principles for (πn)n
Empirical processes indexed by smooth functions
No full textAbstractIn this paper we derive a general invariance principle for empirical processes indexed by smooth functions. The method is applied to prove bounds for the convergence of the empirical distributions which might be useful to verify asymptotic normality of smooth statistical functionals. As one further application we get the convergence of the so-called empirical characteristic function process
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