euclidean {DFA}

euclidean method for detection of crossover points

Description

Applies the euclidean method for detection of crossover points on the log-log curve.

Usage

euclidean(x,y,npoint)

Arguments

x

Vector of the decimal logarithm of the boxes sizes.

y

Vector of the decimal logarithm of the DFA calculated in each boxe.

npoint

Number of crossover points calculated on the log-log curve.

Value

position

Position of the crossover point identified by the euclidean method.

sugestion_before

Sugestion for the position of the second crossover point identified by the euclidean method and calculated in the area before the first crossover point.

sugestion_after

Sugestion for the position of the second crossover point identified by the euclidean method and calculated in the area after the first crossover point.

Author(s)

Victor Barreto Mesquita

References

https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line

Examples

# Example with crossover point fixed in position=20.

library(DFA)
data(lrcorrelation)
x<-lrcorrelation$`log10(boxes)`
y<-c(lrcorrelation$`log10(DFA(alpha = 0.1))`[1:20],lrcorrelation$`log10(DFA(alpha = 0.3))`[21:40])
plot(x,y,xlab="log10(boxes)",ylab="log10(DFA)",pch=19)
fit<- lm(y[1:20] ~ x[1:20])
fit2<-lm(y[21:40] ~ x[21:40])
abline(fit,col="blue")
abline(fit2,col="red")
euclidean(x,y,npoint=1)

# Example with crossover point fixed in position=13 and 26.
library(DFA)
data(lrcorrelation)
x<-lrcorrelation$`log10(boxes)`
y<-c(lrcorrelation$`log10(DFA(alpha = 0.2))`[1:13],lrcorrelation$`log10(DFA(alpha = 0.6))`[14:26]
  ,lrcorrelation$`log10(DFA(alpha = 0.9))`[27:40])
plot(x,y,xlab="log10(boxes)",ylab="log10(DFA)",pch=19)
fit<- lm(y[1:13] ~ x[1:13])
fit2<-lm(y[14:26] ~ x[14:26])
fit3<-lm(y[27:40] ~ x[27:40])
abline(fit,col="blue")
abline(fit2,col="red")
abline(fit3,col="brown")
euclidean(x,y,npoint=2)