On detecting and quantification of randomness for one-sided sequences
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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 of randomness based on frequency analysis of two-sided and one-sided sequences. In addition, the paper suggests an extension of the notion of bandlimitiness on one-sided sequences and a procedure allowing to represent an one-sided sequence as a sum of left-bandlimited and predictable sequences and a non-reducible noise.
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Dokuchaev, Nikolai (2012)The paper suggests a notion of left band-limitness for one-sided semi-infinite sequences representing traces of two-sided band-limited sequences. A method of detecting these sequences is obtained. For more general one-sided ...
Dokuchaev, Nikolai (2017)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 ...
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 ...