A top–bottom price approach to understanding financial fluctuations

• Published in: Physica A 2012-02, Vol.391 (4), p.1489-1496
• Main Authors: Rivera-Castro, Miguel A., Miranda, José G.V., Borges, Ernesto P., Cajueiro, Daniel O., Andrade, Roberto F.S.
• Format: Article
• Language: English
• Subjects: Falling; Fluctuation; Gaussian; Kernels; Markets; Return interval; Smoothing kernel; Statistics; Switching; Switching point; Volatility; Waiting time
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2011.11.022

The presence of sequences of top and bottom (TB) events in financial series is investigated for the purpose of characterizing such switching points. They clearly mark a change in the trend of rising or falling prices of assets to the opposite tendency, are of crucial importance for the players’ decision and also for the market stability. Previous attempts to characterize switching points have been based on the behavior of the volatility and on the definition of microtrends. The approach used herein is based on the smoothing of the original data with a Gaussian kernel. The events are identified by the magnitude of the difference of the extreme prices, by the time lag between the corresponding events (waiting time), and by the time interval between events with a minimal magnitude (return time). Results from the analysis of the inter day Dow Jones Industrial Average index (DJIA) from 1928 to 2011 are discussed. q-Gaussian functions with power law tails are found to provide a very accurate description of a class of measures obtained from the series statistics. ► Top–bottom approach based on a Gaussian kernel to characterize switching points. ► Characterizes the magnitude of the difference between successive extreme prices. ► Provides statistics of waiting time, i.e., time lag between events. ► Considers also return time, time lag between events with a minimal magnitude. ► Distribution probabilities have been accurately adjusted by q-Gaussians.