pracma (version 1.5.8)

hurst: Hurst Exponent

Description

Calculates the Hurst exponent using R/S analysis.

Usage

hurstexp(x, d = 50, display = TRUE)
  hurst(x)

Arguments

x

a time series.

d

smallest box size; default 50.

display

logical; shall the results be printed to the console?

Value

• hurst(x) returns the Hurst exponent. hurstexp(x) returns a list with the following components:
  • Hrs- corrected R over S Hurst exponent
  • Ht- theoretical Hurst exponent
  • Hal- corrected empirical Hurst exponent
  • He- empirical Hurst exponent

Details

hurst(x) calculates the Hurst exponent of time series x using R/S analysis after Hurst. hurstexp(x) corrects it with a small sample bias, see Weron.

Optimal sample sizes are automatically computed with a length that possesses the most divisors among series shorter than x by no more than 1 percent.

References

H.E.Hurst (1951) Long-term storage capacity of reservoirs, Transactions of the American Society of Civil Engineers 116, 770-808.

R.Weron (2002) Estimating long range dependence: finite sample properties and confidence intervals, Physica A 312, 285-299.

See Also

fractal::hurstSpec, RoverS, hurstBlock

Examples

##  Computing the Hurst exponent
data(brown72)
hurst(brown72)                       # 0.7385   # 0.720
hurstexp(brown72, d = 128)
# Corrected R over S Hurst exponent:   0.738 
# Theoretical Hurst exponent:          0.529
# Corrected empirical Hurst exponent:  0.684 
# Empirical Hurst exponent:            0.707 

##  Compare with other implementations
library(fractal)
x72 <- brown72                          #  H = 0.72
xgn <- rnorm(1024)                      #  H = 0.50
xlm <- numeric(1024); xlm[1] <- 0.1     #  H = 0.43
for (i in 2:1024) xlm[i] <- 4 * xlm[i-1] * (1 - xlm[i-1])

x <- x72
hurstSpec(x)                    # 0.776   # 0.720
RoverS(x)                       # 0.717
hurstBlock(x, method="aggAbs")  # 0.648
hurstBlock(x, method="aggVar")  # 0.613
hurstBlock(x, method="diffvar") # 0.714
hurstBlock(x, method="higuchi") # 1.001

x <- xgn
hurstSpec(x)                    # 0.538   # 0.500
RoverS(x)                       # 0.663
hurstBlock(x, method="aggAbs")  # 0.463
hurstBlock(x, method="aggVar")  # 0.430
hurstBlock(x, method="diffvar") # 0.471
hurstBlock(x, method="higuchi") # 0.574

x <- xlm
hurstSpec(x)                    # 0.478   # 0.430
RoverS(x)                       # 0.622
hurstBlock(x, method="aggAbs")  # 0.316
hurstBlock(x, method="aggVar")  # 0.279
hurstBlock(x, method="diffvar") # 0.547
hurstBlock(x, method="higuchi") # 0.998