Maximum entropy for periodically correlated processes from nonconsecutive autocovariance coefficients
نویسنده
چکیده
We consider the maximum entropy extention of a partially specified autocovariance sequence of a periodically correlated process. The sequence may be specified on a non-contiguous set. We give a method which solves the problem completely—it gives the positive definite solution when it exists and reports that it does not exist otherwise. The method is numerically reliable even when the solution is “almost” semidefinite. It also works when only positive semidefinite extention(s) exist.
منابع مشابه
Extension of Autocovariance Coefficients Sequence for Periodically Correlated Processes
The extension of stationary process autocorrelation coefficient sequence is a classical problem in the field of spectral estimation. In this note, we treat this extension problem for the periodically correlated processes by using the partial autocorrelation function. We show that the theory of the non-stationary processes can be adapted to the periodically correlated processes. The partial auto...
متن کاملConvergence Rate of Empirical Autocovariance Operators in H-Valued Periodically Correlated Processes
This paper focuses on the empirical autocovariance operator of H-valued periodically correlated processes. It will be demonstrated that the empirical estimator converges to a limit with the same periodicity as the main process. Moreover, the rate of convergence of the empirical autocovariance operator in Hilbert-Schmidt norm is derived.
متن کاملOn the existence of Hilbert valued periodically correlated autoregressive processes
In this paper we provide sufficient condition for existence of a unique Hilbert valued ($mathbb{H}$-valued) periodically correlated solution to the first order autoregressive model $X_{n}=rho _{n}X_{n-1}+Z_{n}$, for $nin mathbb{Z}$, and formulate the existing solution and its autocovariance operator. Also we specially investigate equivalent condition for the coordinate process...
متن کاملSHIFT OPERATOR FOR PERIODICALLY CORRELATED PROCESSES
The existence of shift for periodically correlated processes and its boundedness are investigated. Spectral criteria for these non-stationary processes to have such shifts are obtained.
متن کاملPeriodically correlated and multivariate symmetric stable processes related to periodic and cyclic flows
In this work we introduce and study discrete time periodically correlated stable processes and multivariate stationary stable processes related to periodic and cyclic flows. Our study involves producing a spectral representation and a spectral identification for such processes. We show that the third component of a periodically correlated stable process has a component related to a...
متن کامل