Forbidden patterns in financial time series

TL;DR

This paper investigates forbidden patterns in financial time series, demonstrating their potential to distinguish deterministic chaos from randomness in economic indicators using permutation entropy.

Contribution

It introduces the application of forbidden pattern analysis to various financial indicators, highlighting its effectiveness with small datasets and its ability to reveal deterministic behavior.

Findings

Forbidden patterns vary across different financial indicators.

Evidence of deterministic behavior in stock indices and bonds.

Permutation entropy helps differentiate chaos from randomness.

Abstract

The existence of forbidden patterns, i.e., certain missing sequences in a given time series, is a recently proposed instrument of potential application in the study of time series. Forbidden patterns are related to the permutation entropy, which has the basic properties of classic chaos indicators, thus allowing to separate deterministic (usually chaotic) from random series; however, it requires less values of the series to be calculated, and it is suitable for using with small datasets. In this Letter, the appearance of forbidden patterns is studied in different economical indicators like stock indices (Dow Jones Industrial Average and Nasdaq Composite), NYSE stocks (IBM and Boeing) and others (10-year Bond interest rate), to find evidences of deterministic behavior in their evolutions.