Negative powers in Lomb-Scargle periodogram

I’ve been using Astropy’s Lomb-Scargle periodogram for some time but just run into an unexpected scenario. I’ve attached a simple series of 19440 points of Gaussian noise (WN_1000_timeseries.txt), generated using 1000*numpy.random.randn(19440). When I compute the Lomb-Scargle periodogram, however, the second-last element has negative power. I was under the impression that this wasn’t possible but I appreciate that I may well be wrong, in which case this issue can be resolved by me understanding the LS periodogram better!

The timeseries is attached and this snippet of code produces the negative value for me.

import numpy as np
from astropy.stats import LombScargle

y = np.loadtxt('WN_1000_timeseries.txt')
f, p = LombScargle(np.arange(len(y), dtype=float), y, center_data=False).autopower(normalization='psd', samples_per_peak=1, nyquist_factor=1)
print(p[-2]) # -2493.908823582499

I’m running Python 3.7.2 on Fedora 29, with NumPy 1.16.0 and Astropy 3.1.2.

[jakevdp]

The default computational approach is an approximation that speeds the algorithm from O[N^2] to O[N log N], at the expense of not producing exact results. For values close to zero, this approximation can lead to negative powers.

If exact results are important to you, you can specify the method argument of the autopower function to something other than "fast".

[jakevdp]

For what it’s worth, I don’t think 1% inaccuracies at high frequencies are worth worrying about. In practice, the signal at such frequencies is so dominated by aliasing effects that a 1% inaccuracy is not going to make any substantive difference in the interpretation of periodograms.