Generalized spectral tests for the martingale difference hypothesis

^aThis article proposes a test for the Martingale Difference Hypothesis (MDH) using dependence measures related to the characteristic function. The MDH typically has been tested using the sample autocorrelations or in the spectral domain using the periodogram. Tests based on these statistics are inconsistent against uncorrelated non-martingales processes. Here, we generalize the spectral test of Durlauf (1991) for testing the MDH taking into account linear and nonlinear dependence. Our test considers dependence at all lags and is consistent against general pairwise nonparametric Pitman's local alternatives converging at the parametric rate n^(-1/2), with n the sample size. Furthermore, with our methodology there is no need to choose a lag order, to smooth the data or to formulate a parametric alternative. Our approach can be easily extended to specification testing of the conditional mean of possibly nonlinear models. The asymptotic null distribution of our test depends on the data generating process, so a bootstrap procedure is proposed and theoretically justified. Our bootstrap test is robust to higher order dependence, in particular to conditional heteroskedasticity. A Monte Carlo study examines the finite sample performance of our test and shows that it is more powerful than some competing tests. Finally, an application to the S and P 500 stock index and exchange rates highlights the merits of our approach

Determining WWW User's Next Access and Its Application to Pre-fetching

World-Wide Web (WWW) services have grown to levels where significant delays are expected to happen. Techniques like pre-fetching are likely to help users to personalize their needs, reducing their waiting times. However, pre-fetching is only effective if the right documents are identified and if user's move is correctly predicted. Otherwise, pre-fetching will only waste bandwidth. Therefore, it is productive to determine whether a revisit will occur or not, before starting pre-fetching. In this paper we develop two user models that help determining user's next move. One model uses Random Walk approximation and the other is based on Digital Signal Processing techniques. We also give hints on how to use such models with a simple pre-fetching technique that we are developing.CNP

Small clique number graphs with three trivial critical ideals

The critical ideals of a graph are the determinantal ideals of the generalized Laplacian matrix associated to a graph. In this article we provide a set of minimal forbidden graphs for the set of graphs with at most three trivial critical ideals. Then we use these forbidden graphs to characterize the graphs with at most three trivial critical ideals and clique number equal to 2 and 3.Comment: 33 pages, 3 figure

Wiggly tails: a gravitational wave signature of massive fields around black holes

Massive fields can exist in long-lived configurations around black holes. We examine how the gravitational wave signal of a perturbed black hole is affected by such `dirtiness' within linear theory. As a concrete example, we consider the gravitational radiation emitted by the infall of a massive scalar field into a Schwarzschild black hole. Whereas part of the scalar field is absorbed/scattered by the black hole and triggers gravitational wave emission, another part lingers in long-lived quasi-bound states. Solving numerically the Teukolsky master equation for gravitational perturbations coupled to the massive Klein-Gordon equation, we find a characteristic gravitational wave signal, composed by a quasi-normal ringing followed by a late time tail. In contrast to `clean' black holes, however, the late time tail contains small amplitude wiggles with the frequency of the dominating quasi-bound state. Additionally, an observer dependent beating pattern may also be seen. These features were already observed in fully non-linear studies; our analysis shows they are present at linear level, and, since it reduces to a 1+1 dimensional numerical problem, allows for cleaner numerical data. Moreover, we discuss the power law of the tail and that it only becomes universal sufficiently far away from the `dirty' black hole. The wiggly tails, by constrast, are a generic feature that may be used as a smoking gun for the presence of massive fields around black holes, either as a linear cloud or as fully non-linear hair.Comment: 6 pages, 4 figure