On detecting predictability of one-sided sequences
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We consider predicting and predictability for discrete time processes in a pathwise setting where only a sole one-sided semi-infinite sequence of past values is available, and where statistical properties of the ensemble of the paths are unknown. We obtain some sufficient conditions of predictability in the terms of degeneracy of frequency characteristics representing one-sided modifications of the Z-transform. These characteristics are defined for one-sided semi-infinite sequences representing of the past values. Some predictors are discussed.
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Dokuchaev, Nikolai (2016)The paper studies discrete time processes and their predictability and randomness in deterministic pathwise setting, without using probabilistic assumptions on the ensemble. We suggest some approaches to quantification ...
Dokuchaev, Nikolai (2018)The paper suggests a method of extrapolation of notion of one-sided semi-infinite sequences representing traces of two-sided band-limited sequences; this features ensure uniqueness of this extrapolation and possibility ...
Dokuchaev, Nikolai (2014)The paper studies frequency characteristics and predictability of real sequences, i.e., discrete time processes in deterministic setting. We consider band-limitness and predictability of one-sided sequences. We establish ...