Propriétés du spectre évolutif d'un processus non stationnaire
QMLE of periodic bilinear models and of PARMA models with periodic bilinear innovations
This paper develops an asymptotic inference theory for bilinear time series models with periodic coefficients . For this purpose, we establish firstly a necessary and sufficient conditions for such models to have a unique stationary and ergodic solutions (in periodic sense). Secondly, we examine the consistency and the asymptotic normality of the quasi-maximum likelihood estimator under very mild moment condition for the innovation errors. As a result, it is shown that whenever the model is...
Ramanujan-Fourier series and the conjecture D of Hardy and Littlewood
We give a heuristic proof of a conjecture of Hardy and Littlewood concerning the density of prime pairs to which twin primes and Sophie Germain primes are special cases. The method uses the Ramanujan-Fourier series for a modified von Mangoldt function and the Wiener-Khintchine theorem for arithmetical functions. The failing of the heuristic proof is due to the lack of justification of interchange of certain limits. Experimental evidence using computer calculations is provided for the plausibility...
Regresión espectral sesgada.
Se propone un método de regresión espectral adecuado cuando los regresores tienen potencia espectral despreciable sobre bandas de frecuencia estrechas. Se investiga la relación entre el método propuesto y los procedimientos de regresión sesgada habituales en el dominio del tiempo.
Robust mixing.
Schätzen der Kovarianzdichte stationärer Punktprozesse aus Zählungen.
Siegel's test for periodic components in multiple time series and its application in engineering practice
Some New Time Series Results.
Some results on the spectral analysis of nonstationary time series.
Spectral analysis of ARMA processes by Prony's method
Spectral density estimation for -adic stationary processes
Spectral density estimation for stationary stable random fields
We consider a stationary symmetric stable bidimensional process with discrete time, having the spectral representation (1.1). We consider a general case where the spectral measure is assumed to be the sum of an absolutely continuous measure, a discrete measure of finite order and a finite number of absolutely continuous measures on several lines. We estimate the density of the absolutely continuous measure and the density on the lines.
Spectrum of randomly sampled multivariate ARMA models
The paper is devoted to the spectrum of multivariate randomly sampled autoregressive moving-average (ARMA) models. We determine precisely the spectrum numerator coefficients of the randomly sampled ARMA models. We give results when the non-zero poles of the initial ARMA model are simple. We first prove the results when the probability generating function of the random sampling law is injective, then we precise the results when it is not injective.
Statistical applications for equivariant matrices.
Statistical estimation of higher-order spectral densities by means of general tapering
Given a realization on a finite interval of a continuous-time stationary process, we construct estimators for higher order spectral densities. Tapering and shift-in-time methods are used to build estimators which are asymptotically unbiased and consistent for all admissible values of the argument. Asymptotic results for the fourth-order densities are given. Detailed attention is paid to the nth order case.
The Uniqueness of the Transfer Function of Linear System from Input-Output Observations.
Two special models of processes with time-dependent random parameters
Un point de vue sur l'analyse spectrale descriptive des chroniques
Variances in spectral analysis of membrane noise
Le fluttuazioni di conduttanza di un modello di canale del potassio di una fibra muscolare che segue una cinetica di Hodgkin e Huxley sono state analizzate attraverso l'analisi spettrale indiretta. Sono state confrontate due diverse stime della densità spettrale e le loro rispettive varianze: quella della prima stima considerata è già nota, mentre quella della seconda stima è stata ricavata da noi nelle medesime ipotesi (distribuzione normale). I risultati teorici sono stati confrontati con quelli...
Wavelet estimation of the long memory parameter for Hermite polynomial of gaussian processes
We consider stationary processes with long memory which are non-Gaussian and represented as Hermite polynomials of a Gaussian process. We focus on the corresponding wavelet coefficients and study the asymptotic behavior of the sum of their squares since this sum is often used for estimating the long–memory parameter. We show that the limit is not Gaussian but can be expressed using the non-Gaussian Rosenblatt process defined as a Wiener–Itô integral of order 2. This happens even if the original...