1,721,063 research outputs found
Surveillance of the covariance matrix based on the properties of the singular Wishart distribution
No full textBayesian inference of the multi-period optimal portfolio for an exponential utility
No full textWe consider the estimation of the multi-period optimal portfolio obtained by maximizing an exponential utility. Employing the Jeffreys non-informative prior and the conjugate informative prior, we derive stochastic representations for the optimal portfolio weights at each time point of portfolio reallocation. This provides a direct access not only to the posterior distribution of the portfolio weights but also to their point estimates together with uncertainties and their asymptotic distributions. Furthermore, we present the posterior predictive distribution for the investor's wealth at each time point of the investment period in terms of a stochastic representation for the future wealth realization. This in turn makes it possible to use quantile-based risk measures or to calculate the probability of default, i.e the probability of the investor wealth to become negative. We apply the suggested Bayesian approach to assess the uncertainty in the multi-period optimal portfolio by considering assets from the FTSE 100 in the weeks after the British referendum to leave the European Union. The behaviour of the novel portfolio estimation method in a precarious market situation is illustrated by calculating the predictive wealth, the risk associated with the holding portfolio, and the probability of default in each period.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Statistic
Optimal shrinkage-based portfolio selection in high dimensions
Get PDFIn this paper we estimate the mean-variance portfolio in the high-dimensional
case using the recent results from the theory of random matrices. We construct
a linear shrinkage estimator which is distribution-free and is optimal in the
sense of maximizing with probability the asymptotic out-of-sample expected
utility, i.e., mean-variance objective function for different values of risk
aversion coefficient which in particular leads to the maximization of the
out-of-sample expected utility and to the minimization of the out-of-sample
variance.
One of the main features of our estimator is the inclusion of the estimation
risk related to the sample mean vector into the high-dimensional portfolio
optimization. The asymptotic properties of the new estimator are investigated
when the number of assets and the sample size tend simultaneously to
infinity such that . The results are obtained
under weak assumptions imposed on the distribution of the asset returns, namely
the existence of the moments is only required.
Thereafter we perform numerical and empirical studies where the small- and
large-sample behavior of the derived estimator is investigated. The suggested
estimator shows significant improvements over the existent approaches including
the nonlinear shrinkage estimator and the three-fund portfolio rule, especially
when the portfolio dimension is larger than the sample size. Moreover, it is
robust to deviations from normality.Comment: 45 pages, UPDATE3: revised version of the manuscript accepted by
Journal of Business and Economic Statistics. substantially revised:
Ledoit-Wolf and Kan-Zhou estimators were added, conditions weakened, proofs
revised, discussion on the Moore-Penrose approximation included, mistake in
the shrinkage formula for c>1 corrected (big boost in performance as a
result
Dynamic Shrinkage Estimation of the High-Dimensional Minimum-Variance Portfolio
No full textIn this paper, new results in random matrix theory are derived, which allow us to construct a shrinkage estimator of the global minimum variance (GMV) portfolio when the shrinkage target is a random object. More specifically, the shrinkage target is determined as the holding portfolio estimated from previous data. The theoretical findings are applied to develop theory for dynamic estimation of the GMV portfolio, where the new estimator of its weights is shrunk to the holding portfolio at each time of reconstruction. Both cases with and without overlapping samples are considered in the paper. The non-overlapping samples corresponds to the case when different data of the asset returns are used to construct the traditional estimator of the GMV portfolio weights and to determine the target portfolio, while the overlapping case allows intersections between the samples. The theoretical results are derived under weak assumptions imposed on the data-generating process. No specific distribution is assumed for the asset returns except from the assumption of finite 4+ɛ, ɛ >0, moments. Also, the population covariance matrix with unbounded largest eigenvalue can be considered. The performance of new trading strategies is investigated via an extensive simulation. Finally, the theoretical findings are implemented in an empirical illustration based on the returns on stocks included in the S&P 500 index.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Statistic
Statische und dynamische Faktormodelle zur Bestimmung der Anzahl der Faktoren
No full textThe variety in factor modelling for multivariate time series implies the necessity to develop the model selection methodology as the 'optimally' chosen model is not only important for understanding the underlying nature of a certain data generating process, but can also be useful in constructing more efficient forecasts. The majority of the methods developed in the literature on factor models consider their time domain representation, meanwhile the frequency domain representation of factor models for multivariate time series offers a number of attractive Features which can be exploited in developing more efficient estimation and/or model selection methods. The present dissertation presents two novel approaches for model selection for dynamic and/or approximate factor models, DFMs and AFMs, respectively, formulated and estimated in the frequency domain. The first approach combines theoretical findings in simultaneous statistical inference with testing common and idiosyncratic factors for autocorrelation. The second approach is based on the recent theoretical findings in the random matrix theory and presents a cross-validatory method of selecting the a optimala number of common factors
Non-parametric Statistical Methods - Applications in MALDI Imaging and Finance
No full textThis thesis contains applications of (non-)parametric statistical methods (and the development of such techniques) with a focus on applications to three distinct topics:
1) Computational statistics, specifically the (efficient and exact) calculation of the joint distribution of order statistics. Since ranks are fundamental to many statistical methods, these have many applications, some of which are detailed.
2) Mathematical finance, specifically results on "reverse stress testing" which, roughly speaking, has the goal of performing a data-driven selection of likely scenarios for which a given portfolio exceeds a specified loss. Two notable contributions are the development of non-parametric confidence regions in elliptical models and a characterisation of the subspace which, in skew-elliptical models, contains the sought scenario.
3) Mathematical statistics, specifically methods with applications to the statistical analysis of biomedical images. One focus is on statistical tests based on correlation coefficients when one of the random variables is a binary random variable. The derived results are utilised to elucidate some statistical properties of matrix-assisted laser desorption/ionization (MALDI) mass spectroscopy data.
In my work on all of these topics, my focus was on developing and applying statistical methods that are based only on the absolutely necessary assumptions. This is, of course, an aspirational goal. I am, however hopeful that I was able to make my own small contribution to the science of mathematical statistics
Recent advances in shrinkage-based high-dimensional inference
No full textRecently, the shrinkage approach has increased its popularity in theoretical and applied statistics, especially, when point estimators for high-dimensional quantities have to be constructed. A shrinkage estimator is usually obtained by shrinking the sample estimator towards a deterministic target. This allows to reduce the high volatility that is commonly present in the sample estimator by introducing a bias such that the mean-square error of the shrinkage estimator becomes smaller than the one of the corresponding sample estimator. The procedure has shown great advantages especially in the high-dimensional problems where, in general case, the sample estimators are not consistent without imposing structural assumptions on model parameters. In this paper, we review the mostly used shrinkage estimators for the mean vector, covariance and precision matrices. The application in portfolio theory is provided where the weights of optimal portfolios are usually determined as functions of the mean vector and covariance matrix. Furthermore, a test theory on the mean–variance optimality of a given portfolio based on the shrinkage approach is presented as well.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Statistic
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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