Significance of log-periodic signatures in cumulative noise

TL;DR

This paper introduces a cumulative Lomb periodogram method to detect and assess the significance of log-periodic signatures in financial market noise, specifically applied to the S&P 500 anti-bubble starting in 2000.

Contribution

It develops a cumulative version of the Lomb periodogram that provides frequency-independent significance testing for log-periodic signals in cumulative noise.

Findings

Successfully applied to S&P 500 data from 2000

Demonstrates the method's ability to identify log-periodic signatures

Provides a statistical significance framework for such signatures

Abstract

Using methods introduced by Scargle in 1978 we derive a cumulative version of the Lomb periodogram that exhibits frequency independent statistics when applied to cumulative noise. We show how this cumulative Lomb periodogram allows us to estimate the significance of log-periodic signatures in the S&P 500 anti-bubble that started in August 2000.