The frequency of pattern occurrence in random walks
In the past decade, the use of ordinal patterns in the analysis of time series and dynamical systems has become an important tool. Ordinal patterns (otherwise known as a permutation patterns) are found in time series by taking $n$ data points at evenly-spaced time intervals and mapping them to a len...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
2015-01-01
|
| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/2476/pdf |
| _version_ | 1797270224660070400 |
|---|---|
| author | Sergi Elizalde Megan Martinez |
| author_facet | Sergi Elizalde Megan Martinez |
| author_sort | Sergi Elizalde |
| collection | DOAJ |
| description | In the past decade, the use of ordinal patterns in the analysis of time series and dynamical systems has become an important tool. Ordinal patterns (otherwise known as a permutation patterns) are found in time series by taking $n$ data points at evenly-spaced time intervals and mapping them to a length-$n$ permutation determined by relative ordering. The frequency with which certain patterns occur is a useful statistic for such series. However, the behavior of the frequency of pattern occurrence is unstudied for most models. We look at the frequency of pattern occurrence in random walks in discrete time, and we define a natural equivalence relation on permutations under which equivalent patterns appear with equal frequency, regardless of probability distribution. We characterize these equivalence classes applying combinatorial methods. |
| first_indexed | 2024-04-25T02:00:52Z |
| format | Article |
| id | doaj.art-a6b6ad6e582d419f9787f27010ebb6c2 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:52Z |
| publishDate | 2015-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-a6b6ad6e582d419f9787f27010ebb6c22024-03-07T15:01:26ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502015-01-01DMTCS Proceedings, 27th...Proceedings10.46298/dmtcs.24762476The frequency of pattern occurrence in random walksSergi Elizalde0Megan Martinez1Department of Mathematics [Dartmouth]Department of Mathematics [Dartmouth]In the past decade, the use of ordinal patterns in the analysis of time series and dynamical systems has become an important tool. Ordinal patterns (otherwise known as a permutation patterns) are found in time series by taking $n$ data points at evenly-spaced time intervals and mapping them to a length-$n$ permutation determined by relative ordering. The frequency with which certain patterns occur is a useful statistic for such series. However, the behavior of the frequency of pattern occurrence is unstudied for most models. We look at the frequency of pattern occurrence in random walks in discrete time, and we define a natural equivalence relation on permutations under which equivalent patterns appear with equal frequency, regardless of probability distribution. We characterize these equivalence classes applying combinatorial methods.https://dmtcs.episciences.org/2476/pdfpermutation patternrandom walktime series analysisordinal patternpattern frequency[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Sergi Elizalde Megan Martinez The frequency of pattern occurrence in random walks Discrete Mathematics & Theoretical Computer Science permutation pattern random walk time series analysis ordinal pattern pattern frequency [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | The frequency of pattern occurrence in random walks |
| title_full | The frequency of pattern occurrence in random walks |
| title_fullStr | The frequency of pattern occurrence in random walks |
| title_full_unstemmed | The frequency of pattern occurrence in random walks |
| title_short | The frequency of pattern occurrence in random walks |
| title_sort | frequency of pattern occurrence in random walks |
| topic | permutation pattern random walk time series analysis ordinal pattern pattern frequency [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2476/pdf |
| work_keys_str_mv | AT sergielizalde thefrequencyofpatternoccurrenceinrandomwalks AT meganmartinez thefrequencyofpatternoccurrenceinrandomwalks AT sergielizalde frequencyofpatternoccurrenceinrandomwalks AT meganmartinez frequencyofpatternoccurrenceinrandomwalks |