Simple trigonometric models for narrow-band stationary processes

1982 ◽  
Vol 19 (A) ◽  
pp. 333-343 ◽  
Author(s):  
A. M. Hasofer
Keyword(s):  
Stationary Process ◽  
Finite Interval ◽  
Narrow Band ◽  
Stationary Processes ◽  
Gaussian Stationary Process ◽  
Trigonometric Sum

Over a finite interval, a Gaussian stationary process can be approximated by a finite trigonometric sum, and the error introduced by the approximation can be exactly bounded, as far as the distribution of the upper tail of the maximum is concerned. A simple case is exhibited, where a narrow band process is well approximated by means of a two-term trigonometric representation.

Simple trigonometric models for narrow-band stationary processes

1982 ◽  
Vol 19 (A) ◽  
pp. 333-343
Author(s):  
A. M. Hasofer
Keyword(s):  
Stationary Process ◽  
Finite Interval ◽  
Narrow Band ◽  
Stationary Processes ◽  
Gaussian Stationary Process ◽  
Trigonometric Sum

Over a finite interval, a Gaussian stationary process can be approximated by a finite trigonometric sum, and the error introduced by the approximation can be exactly bounded, as far as the distribution of the upper tail of the maximum is concerned. A simple case is exhibited, where a narrow band process is well approximated by means of a two-term trigonometric representation.

Non-Stationary Processes and Spectrum

1968 ◽  
Vol 20 ◽  
pp. 1203-1206 ◽  
Author(s):  
K. Nagabhushanam ◽  
C. S. K. Bhagavan
Keyword(s):  
Spectral Density ◽  
Density Function ◽  
Stationary Process ◽  
Spectral Density Function ◽  
Stationary Processes ◽  
Gaussian Stationary Process ◽  
Discrete Parameter ◽  
Image Position

In 1964, L. J. Herbst (3) introduced the generalized spectral density Function1for a non-stationary process {X(t)} denned by1where {η(t)} is a real Gaussian stationary process of discrete parameter and independent variates, the (a;)'s and (σj)'s being constants, the latter, which are ordered in time, having their moduli less than a positive number M.

On estimation of parameters of Gaussian stationary processes

1979 ◽  
Vol 16 (03) ◽  
pp. 575-591 ◽  
Author(s):  
Masanobu Taniguchi
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Density ◽  
Stationary Process ◽  
Parametric Family ◽  
Stationary Processes ◽  
Estimation Of Parameters ◽  
Spectral Densities ◽  
Gaussian Stationary Process

In fitting a certain parametric family of spectral densities fθ (x) to a Gaussian stationary process with the true spectral density g (x), we propose two estimators of θ, say by minimizing two criteria D 1 (·), D 2(·) respectively, which measure the nearness of fθ (x) to g (x). Then we investigate some asymptotic behavior of with respect to efficiency and robustness.

On estimation of parameters of Gaussian stationary processes

1979 ◽  
Vol 16 (3) ◽  
pp. 575-591 ◽  
Author(s):  
Masanobu Taniguchi
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Density ◽  
Stationary Process ◽  
Parametric Family ◽  
Stationary Processes ◽  
Estimation Of Parameters ◽  
Spectral Densities ◽  
Gaussian Stationary Process

In fitting a certain parametric family of spectral densities fθ (x) to a Gaussian stationary process with the true spectral density g (x), we propose two estimators of θ, say by minimizing two criteria D1 (·), D2(·) respectively, which measure the nearness of fθ (x) to g (x). Then we investigate some asymptotic behavior of with respect to efficiency and robustness.

On estimation of the integrals of certain functions of spectral density

1980 ◽  
Vol 17 (01) ◽  
pp. 73-83 ◽  
Author(s):  
Masanobu Taniguchi
Keyword(s):  
Continuous Function ◽  
Spectral Density ◽  
Stationary Process ◽  
Asymptotic Variance ◽  
Asymptotic Properties ◽  
Gaussian Stationary Process

Let g(x) be the spectral density of a Gaussian stationary process. Then, for each continuous function ψ (x) we shall give an estimator of whose asymptotic variance is O(n –1), where Φ(·) is an appropriate known function. Also we shall investigate the asymptotic properties of its estimator.

Alternating projections and interpolation of stationary processes

1992 ◽  
Vol 29 (4) ◽  
pp. 921-931 ◽  
Author(s):  
Mohsen Pourahmadi
Keyword(s):  
Missing Values ◽  
Stationary Process ◽  
Dimensional Space ◽  
Stationary Processes ◽  
Finite Dimensional Space ◽  
Alternating Projections ◽  
Von Neumann ◽  
Finite Dimensional ◽  
Explicit Formulae ◽  
Linear Interpolator

By using the alternating projection theorem of J. von Neumann, we obtain explicit formulae for the best linear interpolator and interpolation error of missing values of a stationary process. These are expressed in terms of multistep predictors and autoregressive parameters of the process. The key idea is to approximate the future by a finite-dimensional space.

A note on the asymptotic eigenvalues and eigenvectors of the dispersion matrix of a second-order Stationary Process on a d-dimensional Lattice

1986 ◽  
Vol 23 (02) ◽  
pp. 529-535 ◽  
Author(s):  
R. J. Martin
Keyword(s):  
Time Series ◽  
Stationary Process ◽  
Second Order ◽  
Stationary Time Series ◽  
Stationary Processes ◽  
Dispersion Matrix ◽  
Eigenvalues And Eigenvectors ◽  
Dimensional Lattice ◽  
Stationary Time

A sufficiently large finite second-order stationary time series process on a line has approximately the same eigenvalues and eigenvectors of its dispersion matrix as its counterpart on a circle. It is shown here that this result can be extended to second-order stationary processes on a d-dimensional lattice.

scholarly journals On the central limit theorem and iterated logarithm law for stationary processes

1975 ◽  
Vol 12 (1) ◽  
pp. 1-8 ◽  
Author(s):  
C.C. Heyde
Keyword(s):  
Central Limit ◽  
Stationary Process ◽  
Stationary Processes ◽  
Martingale Differences ◽  
Stationary Increments ◽  
The Central Limit Theorem ◽  
Iterated Logarithm ◽  
Logarithm Law ◽  
Functional Forms ◽  
Iterated Logarithm Law

It has recently emerged that a convenient way to establish central limit and iterated logarithm results for processes with stationary increments is to use approximating martingales with stationary increments. Functional forms of the limit results can be obtained via a representation for the increments of the stationary process in terms of stationary martingale differences plus other terms whose sum telescopes and disappears under suitable norming. Results based on the most general form of such a representation are here obtained.

On estimation of the integrals of certain functions of spectral density

1980 ◽  
Vol 17 (1) ◽  
pp. 73-83 ◽  
Author(s):  
Masanobu Taniguchi
Keyword(s):  
Continuous Function ◽  
Spectral Density ◽  
Stationary Process ◽  
Asymptotic Variance ◽  
Asymptotic Properties ◽  
Gaussian Stationary Process

Let g(x) be the spectral density of a Gaussian stationary process. Then, for each continuous function ψ (x) we shall give an estimator of whose asymptotic variance is O(n–1), where Φ(·) is an appropriate known function. Also we shall investigate the asymptotic properties of its estimator.

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