Testing for unit roots has been among the most heavily researched topics in Econometrics for the last quarter of a century. Much less researched is the equally important issue of the appropriate transformation if any of the variable of interest which should preceed any such testing. In...

We derive the probability limit of the standard Dickey-Fuller-test in the context of an exponential random walk. This result might be useful in interpreting tests for unit roots when the test is inadvertantly applied to the levels of the data when the true random walk is in the logs.

Returns of risky assets are often modelled as the product of a volatility function and standard Gaussian white noise. Long range data cannot be adequately approximated by simple parametric models. The choice is between retaining simple models and segmenting the data, or to use a non-parametric...

The one-way analysis of variance is concerned with comparing the locations of several one-dimensional samples. This paper gives a simple unified semi-graphical and semi-analytical approach to the problem based on approximation intervals for the locations of the samples. The intervals are...

Under fairly weak conditions it is shown that an optimal portfolio choice exists and is unique. It is further shown that this choice is a continuous function of the joint distribution function of the random returns on the assets from which the choice is made.

It is shown how to choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, an efficient method for locally adaptive...

A good robust functional should, if possible, be efficient at the model, smooth, and have a high breakdown point. M-estimators can be made efficient and Fréchet differentiable by choosing appropriate [psi]-functions but they have a breakdown point of at most 1/(p + 1) in p dimensions. On the...