TK95_uneq: Power law noise generator for unequally sampled observation times

Description

Generates power law noise using TK95 according to Timmer and K<U+00F6>nig (1995), with modifications proposed in Uttley, McHardy and Papadakis (2002) for given irregular observation times.

Usage

TK95_uneq(tt, alpha = 1.5)

Arguments

numeric vector: Observation times given.

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: Noise values related to the observation times.

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 K<U+00F6>nig, M. (1995) On Generating Power Law Noise. Astronomy and Astrophysics, 300, 707-710

Uttley, P., McHardy, I. M. and Papadakis, I. E. (2002) Measuring the Broad-Band Power Spectra of Active Galactic Nuclei with RXTE. Monthly Notices of the Royal Astronomical Society, 332 (1), 231-250

Examples

Run this code

# NOT RUN {
# Compare with example in TK95 to see that the power law is much more clear in
# equally sampled data!
set.seed(31)
# Generate power law noise with exponent alpha=1.5:
tt <- sampler(ttype="unif", ps=1, ncycles=2000, npoints=2000)
y <- TK95_uneq(tt, alpha=1.5)

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

# Plot Lomb-Scargle periodogram with log-axes:
temp <- RobPer(cbind(tt,y,1), weighting=FALSE, model="sine", regression="L2",
    periods=2000/seq(2, 1000, 2))
plot(log(seq(2, 1000, 2)/2000), log(temp), main="log-log-Fourier periodogram",
    xlab="log(frequency)", ylab="log(periodogram)")
title(main= "Power Law not so obvious", cex.main=0.8, line=0.5)

# A line with slope -alpha for comparison
abline(a=-10, b=-1.5, col="red")
text(-5, -1.5, expression(alpha==1.5), col="red")
# }