scholarly journals On a Necessary Condition for the Sample Path Continuity of Weakly Stationary Processes

1970 ◽  
Vol 38 ◽  
pp. 103-111 ◽  
Author(s):  
Izumi Kubo
Keyword(s):  
Distribution Function ◽  
Asymptotic Behavior ◽  
Spectral Distribution ◽  
Covariance Function ◽  
Stationary Process ◽  
Sufficient Conditions ◽  
Sample Path ◽  
Necessary Condition ◽  
Stationary Processes ◽  
Spectral Distribution Function

We shall discuss the sample path continuity of a stationary process assuming that the spectral distribution function F(λ) is given. Many kinds of sufficient conditions have been given in terms of the covariance function or the asymptotic behavior of the spectral distribution function.

scholarly journals Sample Properties of Weakly Stationary Processes

1970 ◽  
Vol 39 ◽  
pp. 7-21 ◽  
Author(s):  
T. Kawata ◽  
I. Kubo
Keyword(s):  
Stochastic Process ◽  
Distribution Function ◽  
Spectral Distribution ◽  
Covariance Function ◽  
Stationary Stochastic Process ◽  
Stationary Processes ◽  
Spectral Distribution Function

Let X(t) = X(t,ω), – ∞ < t < ∞, be a stationary stochastic process withand the continuous covariance functionwhere F(x) is the spectral distribution function.

Some new results on the subexponential class

1989 ◽  
Vol 26 (4) ◽  
pp. 892-897 ◽  
Author(s):  
Emily S. Murphree
Keyword(s):  
Distribution Function ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Subexponential Class ◽  
Class Of Functions

A distribution function F on (0,∞) belongs to the subexponential class if the ratio of 1 – F(2)(x) to 1 – F(x) converges to 2 as x →∞. A necessary condition for membership in is used to prove that a certain class of functions previously thought to be contained in has members outside of . Sufficient conditions on the tail of F are found which ensure F belongs to ; these conditions generalize previously published conditions.

scholarly journals Convergence of the empirical spectral distribution function of Beta matrices

Bernoulli ◽  
2015 ◽  
Vol 21 (3) ◽  
pp. 1538-1574 ◽  
Author(s):  
Zhidong Bai ◽  
Jiang Hu ◽  
Guangming Pan ◽  
Wang Zhou
Keyword(s):  
Distribution Function ◽  
Spectral Distribution ◽  
Empirical Spectral Distribution ◽  
Spectral Distribution Function

scholarly journals Asymptotic properties of least-squares estimates of parameters of the spectrum of a stationary non-deterministic time-series

1964 ◽  
Vol 4 (3) ◽  
pp. 363-384 ◽  
Author(s):  
A. M. Walker
Keyword(s):  
Time Series ◽  
Distribution Function ◽  
Spectral Density ◽  
Spectral Distribution ◽  
Asymptotic Properties ◽  
Spectral Density Function ◽  
Absolutely Continuous ◽  
Spectral Distribution Function ◽  
Image Position ◽  
Least Squares Estimates

Let {xt} (t = 0, ±1, ±2 …) be a stationary non-deterministic time series with E(x2t) < ∞, E(xt) = 0, and let its spectrum be continuous (strictly absolutely continuous) so that the spectral distribution function is the spectral density function. It is well known that {xt} then has a unique one-sided movingaverage representation where .

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.

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