A relative information approach to financial time series analysis using binary $N$-grams dictionaries

TL;DR

This paper introduces a novel method for analyzing financial time series using binary N-grams frequency dictionaries and relative entropy to evaluate market data, addressing computational challenges and exploring various quantization techniques.

Contribution

The paper presents a new approach combining binary N-grams and relative entropy for financial data analysis, including discussions on quantization methods and handling finite data lengths.

Findings

Binary N-grams capture market event information.

Relative entropy measures information capacity of financial data.

Method addresses challenges of finite data length.

Abstract

Here we present a novel approach to statistical analysis of financial time series. The approach is based on $n$-grams frequency dictionaries derived from the quantized market data. Such dictionaries are studied by evaluating their information capacity using relative entropy. A specific quantization of (originally continuous) financial data is considered: so called binary quantization. Possible applications of the proposed technique include market event study with the $n$-grams of higher information value. The finite length of the input data presents certain computational and theoretical challenges discussed in the paper. also, some other versions of a quantization are discussed.