Hurst Exponent
Calculates the Hurst exponent using R/S analysis.
hurstexp(x, d = 50, display = TRUE)
x |
a time series. |
d |
smallest box size; default 50. |
display |
logical; shall the results be printed to the console? |
hurstexp(x) calculates the Hurst exponent of a time series x
using R/S analysis, after Hurst, with slightly different approaches, or
corrects it with small sample bias, see for example Weron.
These approaches are a corrected R/S method, an empirical and corrected empirical method, and a try at a theoretical Hurst exponent. It should be mentioned that the results are sometimes very different, so providing error estimates will be highly questionable.
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.
hurstexp(x) returns a list with the following components:
Hs - simplified R over S approach
Hrs - corrected R over S Hurst exponent
He - empirical Hurst exponent
Hal - corrected empirical Hurst exponent
Ht - theoretical Hurst exponent
Derived from Matlab code of R. Weron, published on Matlab Central.
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.
fractal::hurstSpec, RoverS, hurstBlock and fArma::LrdModelling
## Computing the Hurst exponent data(brown72) 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]) hurstexp(brown72, d = 128) # 0.72 # Simple R/S Hurst estimation: 0.6590931 # Corrected R over S Hurst exponent: 0.7384611 # Empirical Hurst exponent: 0.7068613 # Corrected empirical Hurst exponent: 0.6838251 # Theoretical Hurst exponent: 0.5294909 hurstexp(xgn) # 0.50 # Simple R/S Hurst estimation: 0.5518143 # Corrected R over S Hurst exponent: 0.5982146 # Empirical Hurst exponent: 0.6104621 # Corrected empirical Hurst exponent: 0.5690305 # Theoretical Hurst exponent: 0.5368124 hurstexp(xlm) # 0.43 # Simple R/S Hurst estimation: 0.4825898 # Corrected R over S Hurst exponent: 0.5067766 # Empirical Hurst exponent: 0.4869625 # Corrected empirical Hurst exponent: 0.4485892 # Theoretical Hurst exponent: 0.5368124 ## Compare with other implementations ## Not run: library(fractal) 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 ## End(Not run)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.