Algorithmic information theory in the stock market

Abstract

The paper aims to study the various applications of algorithmic complexity on the stock market, and to evaluate the efficiency of each aspect. The efficiency is measured by the compression rate applied to simulated as well as real world data. The approach differs from typical price modelling which is based on an assumed stochastic nature of the market.

This paper first investigates the properties in Kolmogorov complexities which assists in data compression. Next, similarities between financial markets are measured through the change in price signals. The similarities show that the markets do indeed follow a general trend. Lastly, data compression is performed on a similar data set, namely the S&P 500. Newer algorithms such as the Brotli and XZ show promising results, which outperform older compression algorithms. There is a large discrepancy when the data is converted directly into binary instead of ASCII first. As such, in future studies, a multi-level approach of data conversion and compression can be used to improve new and existing price models based on algorithmic complexity.