Order pattern

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The idea behind an ordinal pattern is to look at the order of the values ​​instead of the values ​​themselves. Roughly speaking, a given sequence of values ​​is converted into a series of so-called order patterns that describe the ups and downs in the original sequence. This approach is of great importance in information theory , the dynamic symbolization of time series and an analysis of time series based on this . Then the distribution of the order patterns obtained is the basis of the analysis.

definition

Be the order. A vector has the ordinal pattern if and if . ${\displaystyle d\in \mathbb {N} }$ ${\displaystyle (v_{1},...,v_{d})\in \mathbb {R} ^{d}}$ ${\displaystyle (r_{1},...,r_{d})\in \mathbb {N} ^{d}}$ ${\displaystyle v_{r_{1}}\geq v_{r_{2}}\geq ...\geq v_{r_{d}}}$ ${\textstyle r_{l-1}>r_{l}}$ ${\displaystyle v_{r_{l-1}}=v_{r_{l}}}$

literature

• K. Keller, H. Lauffer: Symbolic analysis of high-dimensional time series. In: Int. J. Bifurcation Chaos. 1999, pp. 2657-2668, doi: 10.1142 / S0218127403008168 .