Book Review: Stationary processes and prediction theory
نویسندگان
چکیده
منابع مشابه
Asymptotic theory for stationary processes
In the study of random processes, dependence is the rule rather than the exception. To facilitate the related statistical analysis, it is necessary to quantify the dependence between observations. In the talk I will briefly review the history of this fundamental problem. By interpreting random processes as physical systems, I will introduce physical and predictive dependence coefficients that q...
متن کاملMemory-Universal Prediction of Stationary Random Processes
We consider the problem of one-step-ahead prediction of a real-valued, stationary, strongly mixing random process fXig1i= 1. The best mean-square predictor of X0 is its conditional mean given the entire infinite past fXig 1 i= 1. Given a sequence of observations X1 X2 XN , we propose estimators for the conditional mean based on sequences of parametric models of increasing memory and of increasi...
متن کاملSequence prediction for non-stationary processes
We address the problem of sequence prediction for nonstationary stochastic processes. In particular, given two measures on the set of one-way infinite sequences over a finite alphabet, consider the question whether one of the measures predicts the other. We find some conditions on local absolute continuity under which prediction is possible.
متن کاملPrediction for Non-Stationary Stochastic Processes – II
A method is presented for extrapolation of time-series which contain time-varying frequency components. The time-series is complex-demodulated at a set of frequencies. The resulting time-frequency time-series are assumed to be time-dependent such that the amplitude and phase change relatively slowly with time. This change is taken into account in the extrapolation. This model of a non-stationar...
متن کاملOptimal Prediction of Generalized Stationary Processes
Methods for solving optimal filtering and prediction problems for the classical stationary processes are well-known since the late forties. Practice often gives rise to what are not classical stationary processes but generalized ones, e.g., to white noise and to many other examples. Hence it is of interest to carry over optimal prediction and filtering methods to them. For arbitrary generalized...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1963
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1963-10910-6