patterndependence {ordinalpattern}

Ordinal Pattern Dependence

Description

Calculates the standard ordinal pattern coefficient and related values

Usage

patterndependence(tsx,tsy,h=2,block=FALSE,first=TRUE)

## S3 method for class 'pattern'
plot(x, ...)
## S3 method for class 'pattern'
print(x, ...)

Arguments

tsx

numeric vector representing the first univariate time series.

tsy

numeric vector representing the second univariate time series.

h

numeric value determining the length of the ordinal pattern.

block

logical value determining whether patterns are calculated on disjoint blocks or overlapping blocks.

first

logical value indicating which observartions are dropped if block == TRUE and the time series length is no multiple of h+1.

x

object of class "pattern", which is the output of patterndependence

...

further arguments passed to the internal plotting function.

Details

The standard ordinal pattern coefficient is a non-parametric and robust measure of dependence between two time series. It is based on ordinal patterns, which are defined as sequences of ranks of h+1 subsequent observations. This sequences of subseqent observations can either move one observation per time or a whole block of h+1 observations. The former is preferred since it uses more information. If one chooses the later, one has to decide whether the first or the last observations are removed in case that the time series length is no multiple of h+1.

Beside the standard ordinal pattern coefficient, which range from -1 to 1, one can also look at the positive and negative ordinal pattern coefficient, which roughly measures wheather there are unsual many identical or opposite patterns in the time series.

The plot function draws both time series and shows the six most frequent coinciding pattern with counts on the right. At the bottom, the location of these coinciding patterns is visualized.

Value

Object of class "pattern" containing the following values:

patterncoef

standard ordinal pattern coefficient.

alpha

positive ordinal pattern coefficient, see details.

beta

negative ordinal pattern coefficient, see details.

numbequal

number of equal ordinal patterns.

numbopposite

number of opposite ordinal patterns.

PatternXz

number of ordinal patterns in first time series.

PatternYz

number or ordinal patterns in second time series.

coding

coding of the ordinal patterns, used in PatternXz and PatternYz.

PatternX

numeric vector representing the time series of patterns in tsx.

PatternY

numeric vector representing the time series of patterns in tsy.

tsx

numeric vector representing the first univariate time series.

tsy

numeric vector representing the second univariate time series.

maxpat

number representing the maximal pattern code.

block

logical value determining whether patterns are calculated on disjoint blocks or overlapping blocks.

h

number of consecutive observations defining one pattern

tablesame

numeric vector representing the number of coinciding patterns, apportioned into different patterns.

tablesame

numeric vector representing the number of reflected patterns, apportioned into different patterns.

indexsame

logic vector indicating whether patterns in both time series coincide.

indexsame

logic vector indicating whether patterns in both time series are reflected.

Author(s)

Alexander Dürre

References

Schnurr, A. (2014): An ordinal pattern approach to detect and to model leverage effects and dependence structures between financial time series, Statistical Papers, vol. 55, 919–931.

Schnurr, A., Dehling, H. (2017): Testing for Structural Breaks via Ordinal Pattern Dependence, Journal of the American Statistical Association, vol. 112, 706–720.

Examples

set.seed(1066)
patternobj <- patterndependence(rnorm(100),rnorm(100))
plot(patternobj)