Bridging stylized facts in finance and data non-stationarities

TL;DR

This paper introduces a method to analyze nonstationary financial data by segmenting it into locally stationary patches, revealing insights into trading volume and price fluctuation behaviors and their underlying distributions.

Contribution

It applies a segmentation technique to characterize nonstationary financial data, providing a detailed statistical analysis of trading volume and price fluctuations, and identifying the log-normal distribution as a good model.

Findings

Trading volume exhibits a slow evolution with a U-shaped profile during trading sessions.

Price fluctuations change more rapidly than trading volume, indicating different underlying dynamics.

Log-normal distribution best fits the long-term trading volume distribution.

Abstract

Employing a recent technique which allows the representation of nonstationary data by means of a juxtaposition of locally stationary patches of different length, we introduce a comprehensive analysis of the key observables in a financial market: the trading volume and the price fluctuations. From the segmentation procedure we are able to introduce a quantitative description of a group of statistical features (stylizes facts) of the trading volume and price fluctuations, namely the tails of each distribution, the U-shaped profile of the volume in a trading session and the evolution of the trading volume autocorrelation function. The segmentation of the trading volume series provides evidence of slow evolution of the fluctuating parameters of each patch, pointing to the mixing scenario. Assuming that long-term features are the outcome of a statistical mixture of simple local forms, we test and compare different probability density functions to provide the long-term distribution of the trading volume, concluding that the log-normal gives the best agreement with the empirical distribution. Moreover, the segmentation of the magnitude price fluctuations are quite different from the results for the trading volume, indicating that changes in the statistics of price fluctuations occur at a faster scale than in the case of trading volume.