# Complex Correlation Approach for High Frequency Financial Data

## TL;DR

This paper introduces a novel complex correlation method based on Hilbert transform for high frequency financial data, capturing lead-lag relations across different scales without prior knowledge, demonstrated on Tokyo Stock Exchange data.

## Contribution

It presents a new approach to analyze high frequency financial data using complex correlation, revealing sectoral components and lead-lag relations through eigenvector analysis.

## Key findings

- Identification of sector and subsector market components.
- Detection of lead-lag relations with small delays.
- Eigenvector analysis reveals sectoral structures even in noise eigenvalues.

## Abstract

We propose a novel approach that allows to calculate Hilbert transform based complex correlation for unevenly spaced data. This method is especially suitable for high frequency trading data, which are of a particular interest in finance. Its most important feature is the ability to take into account lead-lag relations on different scales, without knowing them in advance. We also present results obtained with this approach while working on Tokyo Stock Exchange intraday quotations. We show that individual sectors and subsectors tend to form important market components which may follow each other with small but significant delays. These components may be recognized by analysing eigenvectors of complex correlation matrix for Nikkei 225 stocks. Interestingly, sectorial components are also found in eigenvectors corresponding to the bulk eigenvalues, traditionally treated as noise.