TK95 {RobPer}

Power law noise generator

Description

Generates an equidistant time series of power law noise according to Timmer and König (1995).

Usage

TK95(N = 1000, alpha = 1.5)

Arguments

N

integer value: Length of the generated time series.

alpha

numeric value: Exponent of the power law. White noise has exponent 0, flicker noise (pink noise) has exponent 1, brown noise has exponent 2.

Value

numeric vector: The generated time series.

Note

This function is used in Thieler et al. (2013). See also Thieler, Fried and Rathjens (2016).

Author(s)

Anita M. Thieler with contributions of Uwe Ligges

References

Thieler, A. M., Backes, M., Fried, R. and Rhode, W. (2013): Periodicity Detection in Irregularly Sampled Light Curves by Robust Regression and Outlier Detection. Statistical Analysis and Data Mining, 6 (1), 73-89

Thieler, A. M., Fried, R. and Rathjens, J. (2016): RobPer: An R Package to Calculate Periodograms for Light Curves Based on Robust Regression. Journal of Statistical Software, 69 (9), 1-36, <doi:10.18637/jss.v069.i09>

Timmer, J. and König, M. (1995) On Generating Power Law Noise. Astronomy and Astrophysics, 300, 707-710

See Also

Applied in tsgen by TK95_uneq.

Examples

set.seed(31)
# Generate power law noise with exponent alpha=1.5:
y <- TK95(N=2000, alpha=1.5)
tt <- seq(along=y)

# Show time series:
plot(tt,y, type="l", main="Power Law Noise", xlab="t", ylab="y")

# Plot Fourier periodogram with log-axes:
temp <- spectrum(y, plot=FALSE)
plot(log(temp$freq), log(temp$spec), main="log-log-Fourier periodogram",
    xlab="log(frequency)", ylab="log(periodogram)")

# A line with slope -alpha for comparison
abline(a=8, b=-1.5, col="red")
text(-2, 12, expression(alpha==1.5), col="red")