In cellular automata with memory, the unchanged maps of the conventional cellular automata are applied to cells endowed with memory of their past states in some specified interval. We implement Rule 30 automata with a majority memory and show that using the memory function we can transform quasi-chaotic dynamics of classical Rule 30 into domains of travelling structures with predictable behaviour. We analyse morphological complexity of the automata and classify dynamics of gliders (particle, self-localizations) in memory-enriched Rule 30. We provide formal ways of encoding and classifying glider dynamics using de Bruijn diagrams, soliton reactions and quasi-chemical representations.
IVIE working papers offer in advance the results of economic research under way in order to encourage a discussion process before sending them to scientific journals for their final publication.
We estimate the Expected Shortfall (ES) of four major cryptocurrencies using various error distributions and GARCH-type models for conditional variance. Our aim is to examine which distributions perform better and to check what component of the speci…cation plays a more important role in estimating ES. We evaluate the performance of the estimations using a rolling-window backtesting technique. Our results highlight the importance of estimating the ES of Bitcoin using a generalized GARCH model and a non-normal error distribution with at least two parameters. Though the results for other cryptocurrencies are less clear-cut, heavy-tailed distributions continue to outperform the normal distribution.
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