Density functionals, with an option-pricing application

We present a method of estimating density-related functionals, without prior knowledge of the density’s functional form. The approach revolves around the specification of an explicit formula for a new class of distributions that encompasses many of the known cases in statistics, including the normal, gamma, inverse gamma, and mixtures thereof. The functionals are based on a couple of hypergeometric functions. Their parameters can be estimated, and the estimates then reveal both the functional form of the density and the parameters that determine centering, scaling, etc. The function to be estimated always leads to a valid density, by design, namely, one that is nonnegative everywhere and integrates to 1. Unlike fully nonparametric methods, our approach can be applied to small datasets. To illustrate our methodology, we apply it to finding risk-neutral densities associated with different types of financial options. We show how our approach fits the data uniformly very well. We also find that our estimated densities’ functional forms vary over the dataset, so that existing parametric methods will not do uniformly well

The joint moment generating function of quadratic forms in multivariate autoregressive series - The case with deterministic components

Let {X-t} follow a discrete Gaussian vector autoregression with deterministic components. We derive the exact finite-sample joint moment generating function (MGF) of the quadratic forms that form the basis for the sufficient statistic. The formula is then specialized to the limiting MGF of functionals involving multivariate and univariate Ornstein–Uhlenbeck processes, drifts, and time trends. Such processes arise asymptotically from more general non-Gaussian processes and also from the Gaussian {X-t} and have also been used in areas other than time series,such as the “goodness of fit” literature

Notation in Econometrics:A Proposal for a Standard

This paper proposes a standard for notation in econometrics.It presents a fully integrated and internally consistent framework for notation and abbreviations, which is as close as possible to existing common practice and also obeys ISO regulations.The symbols used are instantly recognizable and interpretable, thus minimizing ambiguity and enhancing reading efficiency.The standard is designed in a exible manner, thus allowing for future extensions.

A comparison of minimum MSE and maximum power for the nearly integrated non-Gaussian model

We study the optimal choice of quasi-likelihoods for nearly integrated,possibly non-normal, autoregressive models. It turns out that the two mostnatural candidate criteria, minimum Mean Squared Error (MSE) and maximumpower against the unit root null, give rise to different optimalquasi-likelihoods. In both cases, the functional specification of theoptimal quasi-likelihood is the same: it is a combination of the truelikelihood and the Gaussian quasi-likelihood. The optimal relativeweights, however, depend on the criterion chosen and are markedlydifferent. Throughout, we base our results on exact limiting distributiontheory. We derive a new explicit expression for the joint density of theminimal sufficient functionals of Ornstein-Uhlenbeck processes, which alsohas applications in other fields, and we characterize its behaviour forextreme values of its arguments. Using these results, we derive theasymptotic power functions of statistics which converge weakly tocombinations of these sufficient functionals. Finally, we evaluatenumerically our computationally-efficient formulae

Testing for and simulating with nonstationarity in econometrics

SIGLEAvailable from British Library Document Supply Centre- DSC:D176995 / BLDSC - British Library Document Supply CentreGBUnited Kingdo