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We propose a novel semi-nonparametric distribution that is feasibly parameterized to represent the non-Gaussianities of the asset return distributions. Our Moments Expansion (ME) density presents gains in simplicity attributable to its innovative polynomials, which are defined by the difference between the nth power of the random variable and the nth moment of the density used as the basis. We show that the Gram-Charlier distribution is a particular case of the ME-type of densities. The latter being more tractable and easier to implement when quadratic transformations are used to ensure positiveness. In an empirical application to asset returns, the ME model outperforms both standard and non-Gaussian GARCH models along several risk forecasting dimensions.

We apply the Atkinson (1970) inequality index to time series of asset returns to offer a novel measure of financial risk consistent with expected-utility theory. This measure is converted to a certainty-equivalent return serving as a performance measure. We extend the Atkinson index to HARA utility and derive closed-form solutions to our measures for a number of preference-return combinations. Further, we establish relationships between risk aversion and the weights assigned to the cumulants of the return distribution for our performance measure. Using data from hedge funds and asset-pricing anomalies, we find that our performance measure contains additional, economically meaningful information.

This paper contributes to the characterization of the probability density of the price returns in some European day-ahead electricity markets (NordPool, APX, Powernext) by fitting flexible and general families of distributions, such as the α-stable, Normal Inverse Gaussian (NIG), Exponential Power (EP), and Asymmetric Exponential Power (AEP) distributions, and comparing their goodness of fit. The α-stable and the NIG systematically outperform the EP and AEP models, but the tail behavior and the skewness are sensitive to the definition of the returns and to the deseasonalization methods. In particular, the logarithmic transform and volatility rescaling tend to dampen the extreme returns.

It is well known that time series of returns are characterized by volatility clustering and excess kurtosis. Therefore, when modelling the dynamic behavior of returns, inference and prediction methods, based on independent and/or Gaussian observations may be inadequate. As bootstrap methods are not, in general, based on any particular assumption on the distribution of the data, they are well suited for the analysis of returns. This paper reviews the application of bootstrap procedures for inference and prediction of financial time series. In relation to inference, bootstrap techniques have been applied to obtain the sample distribution of statistics for testing, for example, autoregressive dynamics in the conditional mean and variance, unit roots in the mean, fractional integration in volatility and the predictive ability of technical trading rules. On the other hand, bootstrap procedures have been used to estimate the distribution of returns which is of interest, for example, for Value at Risk (VaR) models or for prediction purposes. Although the application of bootstrap techniques to the empirical analysis of financial time series is very broad, there are few analytical results on the statistical properties of these techniques when applied to heteroscedastic time series. Furthermore, there are quite a few papers where the bootstrap procedures used are not adequate. Publicado

Non-Gaussian limiting distributions of the rescaling solutions of the heat equation for non-Gaussian initial data with long-range dependence are discribed in terms of their multiple stochastic integral representations.

In the first part of this thesis, I address the classical problem of asset price dynamics based on a new theoretical framework developed for nonequilibrium physical systems. This problem is mainly relevant for two reasons. First, because understanding the true distribution of returns is important for asset allocation, risk management, and option pricing. Second, because in spite of all the effort in determining the origin of non-Gaussian returns no conclusive result has been achieved yet. The most important result of this part is the demostration that the non-Gaussian shape and stable scaling of the returns distribution are due to slow, but significant, fluctuations in volatility. Futhermore, this result suggests that stock price fluctuations are universal, and that return distributions can be described by one functional form. In the second part, I present an empirical study about the execution of large orders in two stock exchanges: the London Stock Exchange, and the Spanish Stock Exchange. This type of orders can cause a tremendous impact because they are larger than the available liquidity in the order book at a time. For this reason, they are split to minimize transaction costs. Market price impact is the basic factor of these costs, so an accurate description of its functional form is necessary to any optimal execution. The most important result in this part is the empirical determination of this functional form in two markets and the finding of a common behavior in both markets that can be summarized into a concave temporary impact, roughly described by a square root function of the hidden order size, and a price reversion after the completion of the hidden order making permanent impact equal to roughly half of the temporary impact.

The reduced form of the local level model with conditionally heteroscedastic GARCH(1,1) noises is analyzed. We show that the IMA-GARCH model is a good alternative but its conditional heteroscedasticity is weaker than this of the unobserved disturbances. Financial support from Project SEJ2006-03919 by the Spanish Government is gratefully acknowledged Publicado

This paper introduces a new family of multivariate distributions based on Gram–Charlier and Edgeworth expansions. This family encompasses many of the univariate semi-non-parametric densities proposed in financial econometrics as marginal of its different formulations. Within this family, we focus on the analysis of the specifications that guarantee positivity to obtain well-defined multivariate semi-non-parametric densities. We compare two different multivariate distributions of the family with the multivariate Edgeworth–Sargan, Normal, Student's t and skewed Student's t in an in- and out-of-sample framework for financial returns data. Our results show that the proposed specifications provide a reasonably good performance, and would therefore be of interest for applications involving the modelling and forecasting of heavy-tailed distributions.

A new bootstrap procedure to obtain prediction densities of returns and volatilities of GARCH processes is proposed. Financial market participants have shown an increasing interest in prediction intervals as measures of uncertainty. Furthermore, accurate predictions of volatilities are critical for many financial models. The advantages of the proposed method are that it allows incorporation of parameter uncertainty and does not rely on distributional assumptions. The finite sample properties are analyzed by an extensive Monte Carlo simulation. Finally, the technique is applied to the Madrid Stock Market index, IBEX-35. Acknowledgements: We are very grateful for their helpful comments by three anonymous referees, the editor Stephen Pollock and seminar participants at the Universities of Valladolid, New South Wales and Canterbury and the June 2001 Time Series Workshop of Arrabida, the September 2001 International Conference on Modelling Volatility (Perth) and the June 2002 International Symposium on Forecasting (Dublin). We are also grateful to Gregorio Serna for providing the data set analyzed in this paper and to Dolores Redondas for helping us with the figures. Financial support was provided by projects DGES PB96-0111 and BEC2002-03720 from the Spanish Government and Cátedra de Calidad from BBVA Publicado

International audience; The work presented in this paper is part of the filedof automatic recognition of radar targets. Thus, for assistancein target recognition, we propose a new approach to extractefficient feature from synthetic aperture radar (SAR) images.The proposed approach deals with a combination of two featuredescriptors obtained from two methods. In the first method,we perform the dual-tree complex wavelet transform (DT-CWT)on SAR image, and then, the complex subbands magnitudesare modeled by a non-Gaussian statistical model. In the secondmethod, we use the scale invariant feature transform (SIFT). Dueto the fact that SIFT descriptor is limited to a huge dimension,we propose to model its statistical behavior using a non-Gaussianstatistical model in order to overcome this limit. The combinationof the resulting Weibull or Gamma statistical parameters for theboth DT-CWT and SIFT methods are selected as a feature vector.To validate our appraoch, the classification results are providedusing Polynomial kernel based support vector machines (SVM)classifier. The experimental results using SAR images databaseshow the benefits of the proposed approach to extract featuredescriptor.