Statistical Significance of Periodicity and Log-Periodicity with Heavy-Tailed Correlated Noise

Details Statistical Significance of Periodicity and Log-Periodicity with Heavy-Tailed Correlated Noise Statistical Significance of Periodicity and Log-Periodicity with Heavy-Tailed Correlated Noise

2001-10-21

arxiv.org/abs/cond-mat/0110445v1

Int. J. Mod. Phys. C 13 (2), 137-170 (2002)

Physics

Condensed Matter

Statistical Mechanics

Latex document of 35 pages including 17 eps figures, in press in Int. J. Mod. Phys. C 13 (2) (2001)

Scientific paper

10.1142/S0129183102003024

We estimate the probability that random noise, of several plausible standard distributions, creates a false alarm that a periodicity (or log-periodicity) is found in a time series. We investigate general situations with non-Gaussian correlated noises and present synthetic tests on the detectability and statistical significance of periodic components. Increasing heavy-tailness (respectively correlations describing persistence) tends to decrease (respectively increase) the false-alarm probability of finding a large spurious Lomb peak. Increasing anti-persistence tends to decrease the false-alarm probability. We also study the interplay between heavy-tailness and long-range correlations. In order to fully determine if a Lomb peak signals a genuine rather than a spurious periodicity, one should in principle characterize the Lomb peak height, its width and its relations to other peaks in the complete spectrum. As a step towards this full characterization, we construct the joint-distribution of the frequency position (relative to other peaks) and of the height of the highest peak of the power spectrum. We also provide the distributions of the ratio of the second highest Lomb peak to the maximum peak. Using the insight obtained by the present statistical study, we re-examine previously reported claims of ``log-periodicity'' and find that the credibility for log-periodicity in 2D-freely decaying turbulence is weakened while it is strengthened for fracture, for the ion-signature prior to the Kobe earthquake and for financial markets.

Affiliated with

Also associated with

No associations

Rating

Statistical Significance of Periodicity and Log-Periodicity with Heavy-Tailed Correlated Noise does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Statistical Significance of Periodicity and Log-Periodicity with Heavy-Tailed Correlated Noise, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Statistical Significance of Periodicity and Log-Periodicity with Heavy-Tailed Correlated Noise will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-292963