Time series and dependent variables
dc.contributor.author | Savit, Robert S. | en_US |
dc.contributor.author | Green, Matthew L. | en_US |
dc.date.accessioned | 2006-04-10T14:43:57Z | |
dc.date.available | 2006-04-10T14:43:57Z | |
dc.date.issued | 1991-05 | en_US |
dc.identifier.citation | Savit, Robert, Green, Matthew (1991/05)."Time series and dependent variables." Physica D: Nonlinear Phenomena 50(1): 95-116. <http://hdl.handle.net/2027.42/29345> | en_US |
dc.identifier.uri | http://www.sciencedirect.com/science/article/B6TVK-46JYFGX-36/2/8cca00205e5bea368f975df026df1c2e | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/29345 | |
dc.description.abstract | We present a new method for analyzing time series which is designed to extract inherent deterministic dependencies in the series. The method is particularly suited to series with broad-band spectra such as chaotic series with or without noise. We derive quantities, [delta]j([var epsilon]), based on conditional probabilities, whose magnitude, roughly speaking, is an indicator of the extent to which the kth element in the series is a deterministic function of the (k - j)th element to within a measurement uncertainty, [var epsilon]. We apply our method to a number of deterministic time series generated by chaotic processes such as the tent, logistic and Henon maps, as well as to sequences of quasi-random numbers. In all cases the [delta]j correctly indicate the expected dependencies. We also show that the [delta]j are robust to the addition of substantial noise in a deterministic process. In addition, we derive a predictability index which is a measure of the extent to which a time series is predictable given some tolerance, [var epsilon]. Finally, we discuss the behavior of the [delta]i as [var epsilon] approaches zero. | en_US |
dc.format.extent | 1425304 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Elsevier | en_US |
dc.title | Time series and dependent variables | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Physics Department, The University of Michigan, Ann Arbor, MI 48109, USA | en_US |
dc.contributor.affiliationum | Physics Department, The University of Michigan, Ann Arbor, MI 48109, USA | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/29345/1/0000413.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1016/0167-2789(91)90083-L | en_US |
dc.identifier.source | Physica D: Nonlinear Phenomena | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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