A NEW METHOD FOR ESTIMATING THE ORDER OF INTEGRATION OF FRACTIONALLY INTEGRATED PROCESSES USING BISPECTRA

The method proposed in this chapter is making use of the bispectrum transformation to estimate the level of integration of a fractionally integrated time series. Bispectrum ransformation transforms the series into a two dimensional frequency space, and thus has higher information content compared to the Geweke-Porter-Hudak method. The bispectrum method is an alternative to the recently proposed wavelet method that transforms the original series into time-frequency (or time-scale) space.Bispectrum, frequency domain, estimation, long memory

On Locally Dyadic Stationary Processes

We introduce the concept of local dyadic stationarity, to account for non-stationary time series, within the framework of Walsh-Fourier analysis. We define and study the time varying dyadic ARMA models (tvDARMA). It is proven that the general tvDARMA process can be approximated locally by either a tvDMA and a tvDAR process.Comment: 27 pages, 2 figure

Simulations of some Doubly Stochastic Poisson Point Processes

International audienceComputer simulations of point processes are important either to verify the results of certain theoretical calculations that can be very awkward at times, or to obtain practical results when these calculations become almost impossible. One of the most common methods for the simulation of nonstationary Poisson processes is random thinning. Its extension when the intensity becomes random (doubly stochastic Poisson processes) depends on the structure of this intensity. If the random density takes only discrete values, which is a common situation in many physical problems where quantum mechanics introduces discrete states, it is shown that the thinning method can be applied without error. We study in particular the case of binary density and we present the kind of theoretical calculations that then become possible. The results of various experiments realized with data obtained by simulation show fairly good agreement with the theoretical calculations

Central Limit Theorems for Wavelet Packet Decompositions of Stationary Random Processes

This paper provides central limit theorems for the wavelet packet decomposition of stationary band-limited random processes. The asymptotic analysis is performed for the sequences of the wavelet packet coefficients returned at the nodes of any given path of the $M$-band wavelet packet decomposition tree. It is shown that if the input process is centred and strictly stationary, these sequences converge in distribution to white Gaussian processes when the resolution level increases, provided that the decomposition filters satisfy a suitable property of regularity. For any given path, the variance of the limit white Gaussian process directly relates to the value of the input process power spectral density at a specific frequency.Comment: Submitted to the IEEE Transactions on Signal Processing, October 200

Fine scale inhomogeneity of wind-wave energy input, skewness, and asymmetry

Analysis of measured sea and lake wind wave data reveals large variability of the wind energy input, as well as the waves skewness and asymmetry. The spatial and temporal third moments alternate in sign over a few wave periods and over a few wavelengths, respectively. Simulation through a 2D Wave Boundary Layer model in which the air flow is modeled by 2nd order Reynolds equations (Chalikov, 1998) conforms to these findings and exposes a rich structure. We found clear correlation of the variations of the skewness and the asymmetry with the wind input

Utilisation de tests basés sur des statistiques d'ordre supérieur dans l'analyse de séries temporelles mesurées dans l'espace

Tests of hypotheses based on Higher Order Statistics (HOS) are reviewed in the particular context of the identification of nonlinear processes in space plasma. The time series under study are associated with the measurements of electric or/and magnetic field components, or/and counting rates of particles. The basic principles of HOS techniques are reviewed. A general and unified procedure is suggested in order to construct statistical tests: (1) for detecting a non-gaussian or transient signal in a gaussian (or non-gaussian) noise, (2) testing a stochastic time series for non-gaussianity (including non-linearity), (3) studying non-linear wave interactions by using the kth-order coherency function. Asymptotic theory of estimates of the kthorder spectra is implemented in a digital signal processing framework. The effectiveness of the signal detection algorithms is demonstrated through computer simulations. Examples of application on the analysis of satellite data are given.Des tests d'hypothèses basés sur des statistiques d'ordre supérieur sont revus dans le contexte particulier de l'identification de processus non-linéaires dans les plasmas spatiaux. Les séries temporelles étudiées sont associées à la mesure de composantes du champ électrique et/ou magnétique d'ondes ou de turbulences, et/ou de données particules. Les principes de base des statistiques d'ordre supérieur sont brièvement rappelés. Une procédure générale et unifiée est suggérée afin de construire des tests statistiques permettant: (1) de détecter des signaux non-gaussiens ou transitoires au sein d'un bruit gaussien (ou non-gaussien), (2) de tester si une série temporelle est associée ou non à un processus stochastique issu d'un processus non-linéaire, (3) d'étudier des interactions non-linéaires à plusieurs ondes par l'utilisation de la fonction de cohérence d'ordre k. La théorie asymptotique des estimés des spectres d'ordre k est mise en oeuvre dans le cas discret. L'efficacité des algorithmes de détection est démontrée par le biais de simulations numériques. Des exemples d'applications à des données satellites sont présentés