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Titlebook: Gaussian and Non-Gaussian Linear Time Series and Random Fields; Murray Rosenblatt Book 2000 Springer Science+Business Media New York 2000

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Finite Automata and Regular Setsollow that of Georgii 1988. The parameter set of the random variables . . ∈ . is a countable infinite set. A typical case would be that in which . is the set of .-dimensional lattice points. The random variables . take values in a measure space . with . a σ7-field of subsets of . could be countable
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Minimum Phase Estimation,uivalent asymptotically in the Gaussian case to maximum likelihood estimates. Consider the stationary ARMA (., .) minimum phase sequence {x.}. with the ξ.’s independent, identically distributed with mean zero and variance σ..
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The Fluctuation of the Quasi-Gaussian Likelihood,otically normal estimates of the unknown parameters of the model. However, in the non-Gaussian context, even though and invertible (that is, minimum phase), the estimates are not efficient. In the nonminimum phase non-Gaussian case the estimates are not even consistent. However, because most estimat
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Random Fields,ollow that of Georgii 1988. The parameter set of the random variables . . ∈ . is a countable infinite set. A typical case would be that in which . is the set of .-dimensional lattice points. The random variables . take values in a measure space . with . a σ7-field of subsets of . could be countable
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Book 2000assical literature in time series analysis, particularly in the Gaussian case. There is a large literature on probabilistic and statistical aspects of these models-to a great extent in the Gaussian context. In the Gaussian case best predictors are linear and there is an extensive study of the asympt
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https://doi.org/10.1007/978-3-642-85706-5se and consider estimation of parameters. Our discussion is an idealization since it is assumed that the scaled density function . of the independent random variables . generating the stationary autoregressive sequence of order . is known. A discussion of ARMA schemes is more complicated but of a similar character and remarks on them will be made.
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