Prediction of stocks: a new way to look at it.

While the traditional $R^{2}$ value is useful to evaluate the quality of a fit, it does not work when it comes to evaluating the predictive power of estimated financial models in finite samples. In this paper we introduce a validated $R_{V}^{2}$ value that is Taylor made for prediction. Based on data from the Danish stock market, using this measure we find that the dividend-price ratio has good predictive power for time horizons between one year and five years. We explain how the $R_{S}^{2}$ s for different time horizons could be compared, respectively, how they must not be interpreted. For our data we can conclude that the quality of prediction is almost the same for the five different time horizons. This is in contradiction to earlier studies based on the traditional $R^{2}$ value, where it has been argued that the predictive power increases with the time horizon up to a horizon of about five or six years. Furthermore, we find that while inflation and interest rate do not add to the predictive power of the dividend-price ratio then last years excess stock return does

Higher-Order Momentum Distributions and Locally Affine LDDMM Registration

To achieve sparse parametrizations that allows intuitive analysis, we aim to represent deformation with a basis containing interpretable elements, and we wish to use elements that have the description capacity to represent the deformation compactly. To accomplish this, we introduce in this paper higher-order momentum distributions in the LDDMM registration framework. While the zeroth order moments previously used in LDDMM only describe local displacement, the first-order momenta that are proposed here represent a basis that allows local description of affine transformations and subsequent compact description of non-translational movement in a globally non-rigid deformation. The resulting representation contains directly interpretable information from both mathematical and modeling perspectives. We develop the mathematical construction of the registration framework with higher-order momenta, we show the implications for sparse image registration and deformation description, and we provide examples of how the parametrization enables registration with a very low number of parameters. The capacity and interpretability of the parametrization using higher-order momenta lead to natural modeling of articulated movement, and the method promises to be useful for quantifying ventricle expansion and progressing atrophy during Alzheimer's disease

Quantum Integration in Sobolev Classes

We study high dimensional integration in the quantum model of computation. We develop quantum algorithms for integration of functions from Sobolev classes $W^r_p([0,1]^d)$ and analyze their convergence rates. We also prove lower bounds which show that the proposed algorithms are, in many cases, optimal within the setting of quantum computing. This extends recent results of Novak on integration of functions from H\"older classes.Comment: Paper submitted to the Journal of Complexity. 28 page

Emerging Vectors of Narratology: Toward Consolidation or Diversification? (A Response)

This is a response to the questions asked by Franco Passalacqua and Federico Pianzola as a follow-up of the 2013 ENN conference. The discussions that originated at the conference  were rich and thought-provoking and so the editors of this special section of «Enthymema» decided to continue the dialogue about the state of the art and the future of narratology

Moving from irrelevant IC reporting to value-relevant IC disclosures: Key learning points from the Danish experience

Purpose – Informed by the findings of a follow-up research study of companies originally involved in the Danish Guideline Project for Intellectual Capital Statements, this paper provides valuable insights for a potential shift from IC reporting, largely informed by an accounting perspective, towards IC-related disclosures. Design/methodology/approach – The paper draws on data obtained from 21 semi-structured interviews with respondents in 16 companies. The respondents were contacted following a genealogical exercise carried out on the 102 companies involved in the Danish Guideline Project between 1999 and 2003. Findings – The interviews suggested a rather critical perspective towards IC reporting using the intellectual capital statement framework. Despite the attempt of the Danish Guideline Project to establish a reporting standard, a range of experiments resulted in changes to the framework’s original structure. Overall, a trend towards more integrated forms of reporting was discernible, in some part being motivated by the need to reduce the levels of reporting overload. Examples of integration designed to legitimise intellectual capital or corporate social responsibility reports, involving issuing them in tandem with a recognised reporting vehicle such as the annual report, were also encountered. Research limitations/implications – The implications of this study are that timely, value-relevant IC disclosures and compliant reporting, primarily for accountability purposes, have the potential to coexist. In addition to the usual limitations of a semi-structured interview research design, respondents’ difficulties in clearly recalling events during the project after some 10-12 years is a further potential limitation. Additionally, the use of Internet-based communication channels for disclosure purposes was in its infancy at the time of the Danish Guideline Project. Originality/value – The paper provides important insights into the mechanisms of intellectual capital disclosure and intellectual capital reporting as seen from a practitioner perspective. Implications relevant to the continued development of integrated reporting are also identified