Schrödinger and Dirac equations for the hydrogen atom, and Laguerre polynomials

It is usually claimed that the Laguerre polynomials were popularized by Schrödinger when creating wave mechanics; however, we show that he did not immediately identify them in studying the hydrogen atom. In the case of relativistic Dirac equations for an electron in a Coulomb field, Dirac gave only approximations, Gordon and Darwin gave exact solutions, and Pidduck first explicitly and elegantly introduced the Laguerre polynomials, an approach neglected by most modern treatises and articles. That Laguerre polynomials were not very popular before their use in quantum mechanics, probably because they had been little used in classical mathematical physics, is confirmed by the fact that, as we show, they had been rediscovered independently several times during the nineteenth century, in published or unpublished studies of Abel, Murphy, Chebyshev, and Laguerre.     

Discrete Euler processes and their applications

This paper introduces discrete Euler processes and shows their application in detecting and forecasting cycles in non‐stationary data where periodic behavior changes approximately linearly in time. A discrete Euler process becomes a classical stationary process if ‘time’ is transformed properly. By moving from one time domain to another, one may deform certain time‐varying data to non‐time‐varying data. With these non‐time‐varying data on the deformed timescale, one may use traditional tools to do parameter estimation and forecasts. The obtained results then can be transformed back to the original timescale. For datasets with an underlying discrete Euler process, the sample M‐spectrum and the spectra estimator of a Euler model (i.e., EAR spectral) are used to detect cycles of a Euler process. Beam response and whale data are used to demonstrate the usefulness of a Euler model. Copyright © 2008 John Wiley & Sons, Ltd.     

Retail default prediction by using sequential minimal optimization technique

This paper employed sequential minimal optimization (SMO) to develop default prediction model in the US retail market. Principal components analysis is used for variable reduction purposes. Four standard credit scoring techniques—naïve Bayes, logistic regression, recursive partitioning and artificial neural network—are compared to SMO, using a sample of 195 healthy firms and 51 distressed firms over five time periods between 1994 and 2002. The five techniques perform well in predicting default particularly one year before financial distress. Furthermore, the prediction still remains sound even 5 years before default. No single methodology has the absolute best classification ability, as the model performance varies in terms of different time periods and variable groups. External influences have greater impacts on the naïve Bayes than other techniques. In terms of similarity with Moody's ranking, SMO excelled over other techniques in most of the time periods. Copyright © 2008 John Wiley & Sons, Ltd.     

For whom the bell tolls? DING proteins in health and disease

DING proteins, identified mainly by their eponymous N-terminal sequences, are ubiquitous in living organisms. Amongst bacteria, they are common in pseudomonads, and have been characterised with respect to genetics and structure. They form part of a wider family of phosphate-binding proteins, with emerging roles in phosphate acquisition and pathogenicity. Many DING proteins have been isolated in eukaryotes, in which they have been associated with very diverse biological activities, often in the context of possible signalling roles. Disease states in which DING proteins have been implicated include rheumatoid arthritis, lithiasis, atherosclerosis, some tumours and tumour-associated cachexia, and bacterial and viral adherence. Complete genetic and structural characterisation of eukaryotic DING genes and proteins is still lacking, though the phosphate-binding site seems to be conserved. Whether as bacterial proteins related to bacterial pathogenicity, or as eukaryotic components of biochemical signalling systems, DING proteins require further study. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Functional methods for time series prediction: a nonparametric approach

The problem of prediction in time series using nonparametric functional techniques is considered. An extension of the local linear method to regression with functional explanatory variable is proposed. This forecasting method is compared with the functional Nadaraya–Watson method and with finite‐dimensional nonparametric predictors for several real‐time series. Prediction intervals based on the bootstrap and conditional distribution estimation for those nonparametric methods are also compared. Copyright © 2010 John Wiley & Sons, Ltd.     

Testing for the usefulness of forecasts

Ashley (Journal of Forecasting 1983; 2 (3): 211–223) proposes a criterion (known as Ashley's index) to judge whether the external macroeconomic variables are well forecast to serve as explanatory variables in forecasting models, which is crucial for policy makers. In this article, we try to extend Ashley's work by providing three testing procedures, including a ratio‐based test, a difference‐based test, and the Bayesian approach. The Bayesian approach has the advantage of allowing the flexibility of adapting all possible information content within a decision‐making environment such as the change of variable's definition due to the evolving system of national accounts. We demonstrate the proposed methods by applying six macroeconomic forecasts in the Survey of Professional Forecasters. Researchers or practitioners can thus formally test whether the external information is helpful. Copyright © 2010 John Wiley & Sons, Ltd.     

A fractionally integrated exponential model for UK unemployment

Fractionally integrated models with the disturbances following a Bloomfield ( 1973 ) exponential spectral model are proposed in this article for modelling UK unemployment. This gives us a better understanding of the low‐frequency dynamics affecting the series without relying on any particular ARMA specification for its short‐run components which, in general, require many more parameters to estimate. The results indicate that this exponential model, confounded with fractional integration, may be a feasible way of modelling unemployment. It also shows that its order of integration is much higher than one and thus leads to the conclusion that the standard practice of taking first differences may lead to erroneous results. Copyright © 2001 John Wiley & Sons, Ltd.     

Do professional forecasters believe in the Phillips curve? evidence from the G7 countries

This paper uses monthly survey data for the G7 countries for the time period 1989–2007 to explore the link between expectations on nominal wages, prices and unemployment rates as suggested by the wage and price Phillips curves. Four major findings stand out. First, we find that survey participants trust in both types of Phillips curve relationships. Second, we find evidence in favor of nonlinearities in the price Phillips curve. Third, we take into account a kink in the price Phillips curve to indicate that the slope of the Phillips curve differs during the business cycle. We find strong evidence of this feature in the data which confirms recent theoretical discussions. Fourth, we employ our data to the expectations‐augmented Phillips curve model. The results suggest that professional forecasters adopt this model when forecasting macroeconomic variables. Copyright © 2010 John Wiley & Sons, Ltd.