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We express the classic ARMA time-series model as a directed graphical model. In doing so, we find that the deterministic re-lationships in the model make it effectively impossible to use the EM algori...
We obtain necessary and sufficient conditions for the existence of strictly stationary solutions of multivariate ARMA equations with independent and identically distributed noise. For general ARMA(p...
In this Pa per we firstly study f, the inverse Laplace transform of F(s) = n,=(,s - 0 3 . The distribution f is then used to define a family of linear distribution processes. This family generalizes ...
This paper describe6 the adaptive estimation problem based on ranks for the parameter of an ARMA process. Tbe local asymptotic normality property with a ranked based central sequence allows for the...
In this paper, motivated by [2], we derive necessary and suficient conditions for bounded and periodically correlated solutions to the system of equations described by ARMA(1, q) model.
This paper is devoted to ARMA models with timedependent coefficients, including well-known periodic ARMA models. We provide state-space representations and Kalman-type recursions to derive a Wold–C...
The Box-Cox transformation has been used as a simple method of transforming dependent variable in ordinary-linear regression circumstances for improving the Gaussian-likelihood fit and making the dist...
A convolution semigroup of probability generating functions and its related operator ⊙F are used to construct a class of stationary Z+-valued autoregressive moving average (ARMA) processes. Several ...
The object of this paper is to study the asymptotic dependence structure of the linear time series models with infinitely divisible innovations by the use of their characteristic functions. Autoregr...
In this paper the stochastic complexity criterion is applied to estimation of the order in AR and ARMA models. The power of the criterion for short strings is illustrated by simulations. It requires...

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