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.

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.

Generalized Levinson–Durbin Sequences and Binomial Coefficients

Integers ◽  
2009 ◽  
Vol 9 (2) ◽  
Author(s):  
Paul Shaman
Keyword(s):  
Stochastic Process ◽  
Sample Size ◽  
Mean Square Error ◽  
Discrete Time ◽  
Minimum Mean Square Error ◽  
Stationary Stochastic Process ◽  
Binomial Coefficients ◽  
Stationary Processes ◽  
Mean Square ◽  
Special Case

AbstractThe Levinson–Durbin recursion is used to construct the coefficients which define the minimum mean square error predictor of a new observation for a discrete time, second-order stationary stochastic process. As the sample size varies, the coefficients determine what is called a Levinson–Durbin sequence. A generalized Levinson–Durbin sequence is also defined, and we note that binomial coefficients constitute a special case of such a sequence. Generalized Levinson–Durbin sequences obey formulas which generalize relations satisfied by binomial coefficients. Some of these results are extended to vector stationary processes.

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 .

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