Noise simulation examples

2019-12-15

Simulating noise types (following this)

library(tuneR)

# White noise
w <- tuneR::noise(kind = c("white"))

# Brown noise is integrated white noise
# (ie. random walk)
# Use same time series length as in the other series
b <- cumsum(rnorm(length(w@left)))

# Pink noise
p <- tuneR::noise(kind = c("pink"))

# Visualize
par(mfrow=c(3,1))
plot(w,main="white noise")
plot(b,main="brown noise")
plot(p,main="pink noise")

Estimating Hurst exponent for the noises

library(pracma)
Hwhite <- hurstexp(w@left, d = 128)

## Simple R/S Hurst estimation:         0.5290583 
## Corrected R over S Hurst exponent:   0.5276734 
## Empirical Hurst exponent:            0.5081172 
## Corrected empirical Hurst exponent:  0.4923274 
## Theoretical Hurst exponent:          0.5155387

Hbrown <- hurstexp(b, d = 128)

## Simple R/S Hurst estimation:         0.9178366 
## Corrected R over S Hurst exponent:   1.012251 
## Empirical Hurst exponent:            1.016203 
## Corrected empirical Hurst exponent:  1.012132 
## Theoretical Hurst exponent:          0.5155387

Hpink <- hurstexp(p@left, d = 128)

## Simple R/S Hurst estimation:         0.8416097 
## Corrected R over S Hurst exponent:   0.9304329 
## Empirical Hurst exponent:            0.9398541 
## Corrected empirical Hurst exponent:  0.9336077 
## Theoretical Hurst exponent:          0.5155387