hurst exponent

gistfile1.scala

import math.{pow, log, sqrt}
import java.util.Random
import org.apache.commons.math.stat.StatUtils.mean
import org.apache.commons.math.stat.regression.SimpleRegression

object HurstExponent extends App {
  
  def hurstExponent(xs: Array[Double]): Double = {
    def S(xs: Array[Double]): Double = {
      val meanXs = mean(xs)
      sqrt(xs.map(x => pow(x - meanXs, 2.0)).sum / xs.length.toDouble)
    }
  
    def R(xs: Array[Double]): Double = {
      val meanXs = mean(xs)
      val newXs = xs.map(_ - meanXs)
      val Z = (1 to xs.length).map(i => newXs.slice(0, i).sum)
      Z.max - Z.min
    }
    
    def Q(xs: Array[Double]): Double = R(xs) / S(xs)

    val logQ = for {
      t <- (1 to log(xs.length).toInt).map(pow(2.0, _).toInt).toArray
    } yield {
      val partXs = xs.slice(0, xs.length - xs.length % t)
      val xss = partXs.grouped(t)
      log(mean(xss.map(xs => Q(xs.toArray)).toArray))
    }

    val logT = (1 to log(xs.length).toInt).map(x => log(pow(2.0, x)))

    val sr = new SimpleRegression()
    for ((a, b) <- (logT zip logQ).filterNot(_._2.isNaN)) {
      sr.addData(a, b)
    }

    sr.getSlope()
  }

  object Random extends Random

  println(hurstExponent(1 to 10000 map(_ => Random.nextDouble() - 0.5) toArray))
}