Wavelets and the generalization of the variogram

The experimental variogram computed in the usual way by the method of moments and the Haar wavelet transform are similar in that they filter data and yield informative summaries that may be interpreted. The variogram filters out constant values; wavelets can filter variation at several spatial scales and thereby provide a richer repertoire for analysis and demand no assumptions other than that of finite variance. This paper compares the two functions, identifying that part of the Haar wavelet transform that gives it its advantages. It goes on to show that the generalized variogram of order k=1, 2, and 3 filters linear, quadratic, and cubic polynomials from the data, respectively, which correspond with more complex wavelets in Daubechies's family. The additional filter coefficients of the latter can reveal features of the data that are not evident in its usual form. Three examples in which data recorded at regular intervals on transects are analyzed illustrate the extended form of the variogram. The apparent periodicity of gilgais in Australia seems to be accentuated as filter coefficients are added, but otherwise the analysis provides no new insight. Analysis of hyerpsectral data with a strong linear trend showed that the wavelet-based variograms filtered it out. Adding filter coefficients in the analysis of the topsoil across the Jurassic scarplands of England changed the upper bound of the variogram; it then resembled the within-class variogram computed by the method of moments. To elucidate these results, we simulated several series of data to represent a random process with values fluctuating about a mean, data with long-range linear trend, data with local trend, and data with stepped transitions. The results suggest that the wavelet variogram can filter out the effects of long-range trend, but not local trend, and of transitions from one class to another, as across boundaries.

Credit flow [poetry]

A poem within the Alhambra Poetry Calendar 2011, a desk calendar and poetry anthology in one.

Stakeholder-defined corporate responsibility for a pre-credit-crunch financial service company: lessons for how good reputations are won and lost

This paper presents a study that identifies a stakeholder-defined concept of Corporate Responsibility (CR) in the context of a UK financial service organisation in the immediate pre-credit crunch era. From qualitative analysis of interviews and focus groups with employees and customers, we identify, in a wide-ranging stakeholder-defined concept of CR, six themes that together imply two necessary conditions for a firm to be regarded as responsible— both corporate actions and character must be consonant with CR. This provides both empirical support for a notable, recent theoretical contribution by Godfrey (in Acad Manag Rev 30:777–798, 2005) and novel lessons for reputation management practice.