Simulation of Real Discrete Time Gaussian Multivariate Stationary Processes with Given Spectral Densities

2015 ◽  
Vol 36 (6) ◽  
pp. 783-796 ◽  
Author(s):  
M. Azimmohseni ◽  
A. R. Soltani ◽  
M. Khalafi
Keyword(s):  
Discrete Time ◽  
Stationary Processes ◽  
Spectral Densities

Estimation of spectral densities of stationary processes

1979 ◽  
Vol 19 (1) ◽  
pp. 47-60
Author(s):  
I. G. Zhurbenko ◽  
N. N. Trush
Keyword(s):  
Stationary Processes ◽  
Spectral Densities

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.

On higher spectral densities of stationary processes with mixing

1976 ◽  
Vol 27 (4) ◽  
pp. 364-373 ◽  
Author(s):  
I. G. Zhurbenko ◽  
N. M. Zuev
Keyword(s):  
Stationary Processes ◽  
Spectral Densities

A power-law model and other models for long-range dependence

1997 ◽  
Vol 34 (3) ◽  
pp. 657-670 ◽  
Author(s):  
R. J. Martin ◽  
A. M. Walker
Keyword(s):  
Long Range ◽  
Discrete Time ◽  
Power Law ◽  
Long Range Dependence ◽  
Stationary Processes ◽  
Power Law Model ◽  
Slow Decay ◽  
Exact Power ◽  
Correlation Structures ◽  
Discrete Time Models

It is becoming increasingly recognized that some long series of data can be adequately and parsimoniously modelled by stationary processes with long-range dependence. Some new discrete-time models for long-range dependence or slow decay, defined by their correlation structures, are discussed. The exact power-law correlation structure is examined in detail.

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